The Fokker-Planck equation. Methods of solution and applications

From MaRDI portal
Publication:797918

zbMath0546.60084MaRDI QIDQ797918

Hannes Risken

Publication date: 1984

Published in: Springer Series in Synergetics (Search for Journal in Brave)




Related Items

The covariant form of the Klein-Kramers equation and the associated moment equations, Modeling of transport in groundwater for environmental risk assessment, Markovian embedding procedures for non-Markovian stochastic Schrödinger equations, Quasilinear approximations for the propagator of the Fokker-Planck equation, Decision-time statistics of nonlinear diffusion models: characterizing long sequences of subsequent trials, Coloured noise analysis of a phase-locked loop system: beyond Itô and Stratonovich stochastic calculi, The entropy production distribution in non-Markovian thermal baths, Stationary properties and stochastic resonance for a saturation laser model with cross-correlation between quantum noise terms, Generalized Schmoluchowski equation, Nonclassical problem for ultraparabolic equation in abstract spaces, The minimal length uncertainty and the nonextensive thermodynamics, Intermittent diffusion in the presence of noise, Error analysis of modified Langevin dynamics, A maximum entropy method for particle filtering, Nonlinear Fokker-Planck-Kolmogorov equation in the semiclassical coherent trajectory approximation, Persistent distribution functions for the dispersion of structured populations, Estimation of the smallest eigenvalue in fractional escape problems: semi-analytics and fits, Fisher information as a measure of time, Connecting the dots: semi-analytical and random walk numerical solutions of the diffusion-reaction equation with stochastic initial conditions, Mean first-passage time in a bistable kinetic model with stochastic potentials, Transport of particles caused by correlated disorder-noise couplings, Asymptotic analysis of nonlinear systems with small stochastic perturbations, Stochastic process semantics for dynamical grammars, A Hopf-like equation and perturbation theory for differential delay equations, Synchronization induced by periodic inputs in finite \(N\)-unit bistable Langevin models: the augmented moment method, Euler-Darboux transformation for the Fokker-Planck equation, Random Lie group actions on compact manifolds: a perturbative analysis, Stochastic \(\varphi^4\)-theory in the strong coupling limit, Information filtering by synchronous spikes in a neural population, On closure methods in nonlinear stochastic dynamics, A chronotopic model of mobility in urban spaces, Effect of correlated noises on Brownian motor, Resonance in a noise-driven excitable neuron model, Passing to the limit in a Wasserstein gradient flow: from diffusion to reaction, Correlation in the velocity of a Brownian particle induced by frictional anisotropy and magnetic field, Study of thermodynamically inspired quantities for both thermal and external colored non-Gaussian noises driven dynamical system, Stock exchange dynamics involving both Gaussian and Poissonian white noises: Approximate solution via a symbolic stochastic calculus., Stochastic optimal control via Bellman's principle., Gravitational wave detection: stochastic resonance method with matched filtering, Colored noise in activated rate processes, Master equations for subordinated processes, The numerical solution of Fokker-Planck equation with radial basis functions (RBFs) based on the meshless technique of Kansa's approach and Galerkin method, Effects of cross-correlation between the real and imaginary parts of the quantum noise in a two-mode saturation laser system, The rule for a subdiffusive particle in an extremely diverse environment, Relaxation to stationary states for anomalous diffusion, Approximate solution for some stochastic differential equations involving both Gaussian and Poissonian white noises, Stochastically perturbed sliding motion in piecewise-smooth systems, Effect of noise and perturbations on limit cycle systems, Fractional Fokker-Planck equation and Black-Scholes formula in composite-diffusive regime, Finite sampling interval effects in Kramers-Moyal analysis, Frequency analysis with coupled nonlinear oscillators, Effect of the noise correlation time on the stationary current of Brownian particle in a spatially symmetric periodic potential, Statistical properties of a turbulent cascade, New approximations and tests of linear fluctuation-response for chaotic nonlinear forced-dissipative dynamical systems, Thermodynamical properties of triangular quantum wires: entropy, specific heat, and internal energy, Tunable transport with broken space-time symmetries, Kraus operator-sum solution to the master equation describing the single-mode cavity driven by an oscillating external field in the heat reservoir, Multiple-scale stochastic processes: decimation, averaging and beyond, Alternative description of stochastic processes in nonlinear systems. ``Kinetic form of master and Fokker-Planck equations, On the connection between linear combination of entropies and linear combination of extremizing distributions, A stochastic model for the dynamics of a classical spin, Phase space reduction of the one-dimensional Fokker-Planck (Kramers) equation, Half-range completeness for the Fokker-Planck equation with an external force, The response of a linear monostable system and its application in parameters estimation for PSK signals, A path integration algorithm for stochastic structural dynamic systems, The diffusion approximation of stochastic evolutionary game dynamics: mean effective fixation time and the significance of the one-third law, Short-time linear response with reduced-rank tangent map, Markov properties of electrical discharge current fluctuations in plasma, On calculus of local fractional derivatives, Langevin equation, Fokker-Planck equation and cell migration, Colored noise induced net voltage of the underdamped Josephson junction, Pseudospectral methods of solution of the Schrödinger equation, Anomalous finite-size effects in the battle of the sexes, From short to fat tails in financial markets: a unified description, Four dimensional Fokker-Planck solver for electron kinetics in collisional gas discharge plasmas, Some results for an \({\mathcal{N}}\)-dimensional nonlinear diffusion equation with radial symmetry, Particle simulation of nonequilibrium gas flows based on ellipsoidal statistical Fokker-Planck model, Escape probability, mean residence time and geophysical fluid particle dynamics, Understanding quantum measurement from the solution of dynamical models, The characteristic noise connected with continuous measurement in classical system without memory, Numerical simulations of stochastic differential equations, Noncoercive convection-diffusion elliptic problems with Neumann boundary conditions, Correlation resonance in noise-driven coupled nonlinear oscillators, Computer simulations of multiplicative stochastic differential equations, Stochastic analyses of the dynamics of generalized Little-Hopfield-Hemmen type neural networks, Stochastic equations of the Langevin type under a weakly dependent perturbation, Diffusion and memory effects for stochastic processes and fractional Langevin equations, Enhancement of signal-to-noise ratio, Linear response and stochastic resonance of superparamagnets, Effect of an exponentially decaying threshold on the firing statistics of a stochastic integrate-and-fire neuron, Exact formula for currents in strongly pumped diffusive systems, The incentive effect of venture capital in bilateral partnership systems with the bias mono-stable Cobb-Douglas utility, Numerical solution of two-dimensional Fokker-Planck equations, Brownian motors: solitary wave and efficiency, A variational principle for the Kramers equation with unbounded external forces, Eigenvalues of the one-dimensional Smoluchowski equation., Turbulence noise., Correlated random walks, hyperbolic systems and Fokker-Planck equations, Single effective neuron: Dendritic coupling effects and stochastic resonance, On the weak-noise limit of Fokker-Planck models, Exact cumulant Kramers-Moyal-like expansion, On the influence of reflective boundary conditions on the statistics of Poisson-Kac diffusion processes, Thermostatistical aspects of generalized entropies, The generalized Langevin equation revisited: analytical expressions for the persistence dynamics of a viscous fluid under a time dependent external force, Ratchet effect in an underdamped periodic potential and its characterisation, Controlling of stochastic resonance and noise enhanced stability induced by harmonic noises in a bistable system, Wealth and price distribution by diffusive approximation in a repeated prediction market, Symmetry of stochastic non-variational differential equations, Stochastical aspects of neuronal dynamics: Fokker-Planck approach, Deterministic and stochastic analysis for different types of regulations in the spontaneous emergence of cell polarity, How does transient signaling input affect the spike timing of postsynaptic neuron near the threshold regime: an analytical study, A mean field approximation in data assimilation for nonlinear dynamics, Adaptive deep density approximation for Fokker-Planck equations, Black-Scholes like closed form formulas and numerical solutions for American style options, Transport and diffusion of Brownian particles in a tilted deformable potential, Analytical solution of diffusion probability for a flat potential with a localized sink, Irreversibility and entropy production of a thermally driven micromachine, Modeling the lake eutrophication stochastic ecosystem and the research of its stability, Supersymmetry and Fokker-Planck dynamics in periodic potentials, Dynamical properties of subdiffusion in the bistable system with aperiodic inputs, Equilibrium of a Brownian particle with coordinate dependent diffusivity and damping: generalized Boltzmann distribution, Automated first and second order moment equations for a set of stochastic differential equations of type \({\mathbf A}\dot{\mathbf Z} + {\mathbf {BZ}} = {\mathbf C}(t)\), The solution of direct and inverse fractional advection-dispersion problems by using orthogonal collocation and differential evolution, Bounds of the entropy production of the irreversible thermodynamics and its relation with the non-equilibrium temperature, Numerical solution of differential equations with colored noise, Investigation on the enhancement phenomenon of biased-diffusion in periodic potential, Kernel methods for the approximation of some key quantities of nonlinear systems, Sentiment contagion analysis of interacting investors: evidence from China's stock forum, The long time behavior of Brownian motion in tilted periodic potentials, Can quantum fluctuation enhance diffusion in a corrugated plane?, Langevin thermostat for robust configurational and kinetic sampling, On the fundamental solution and a variational formulation for a degenerate diffusion of Kolmogorov type, Infinitive operator-sum representation for damping in a squeezed heat reservoir via the thermo entangled state approach, Nonexistence of global solutions for a class of two-time nonlinear evolution equations, Population genetics with fluctuating population sizes, Periodic Airy process and equilibrium dynamics of edge fermions in a trap, A method for the calculation of characteristics for the solution to stochastic differential equations, A parameter estimation method using linear response statistics, Power spectrum of a noisy system close to a heteroclinic orbit, Dynamic stochastic resonance-based grayscale logo extraction in hybrid SVD-DCT domain, LWT-DSR based new robust framework for watermark extraction under intentional attack conditions, A high-order fully conservative block-centered finite difference method for the time-fractional advection-dispersion equation, A non-perturbative analytic expression of signal amplification factor in stochastic resonance, A probabilistic framework for the control of systems with discrete states and stochastic excitation, Irreversible dynamics of Abrikosov vortices in type-two superconductors, Non-local velocity distribution function and one-flight approximation, Time-dependent solutions of the Fokker-Planck equation of maximally reduced air-sea coupling climate model, Ket-Bra entangled state method for solving master equation of finite-level system, Statistical structure of neural spiking under non-Poissonian or other non-white stimulation, Information filtering in resonant neurons, The dynamics of memory retrieval in hierarchical networks, Information filtering by coincidence detection of synchronous population output: analytical approaches to the coherence function of a two-stage neural system, Stochastic (in)stability of synchronisation of oscillators on networks, Coarse-graining Langevin dynamics using reduced-order techniques, Complex-valued Wiener measure: An approach via random walk in the complex plane, A Langevin equation for the energy cascade in fully developed turbulence, Homoclinic tangencies and non-normal Jacobians-effects of noise in nonhyperbolic chaotic systems, Scalar transport in compressible flow, Evolution of randomly perturbed sine-Gordon kink, Exact solutions of a Fokker-Planck equation., On the stationary distribution of self-sustained oscillators around bifurcation points., Diffusion in a periodic potential with a local perturbation., Numerical solution for Fokker-Planck equations in accelerators, Statistical field theory of a nonadditive system, Characterization of stationary distributions using conditional expectations, Path integral solutions of the governing equation of SDEs excited by Lévy white noise, Fluctuations in a nonlinear laser field with coupling of additive noise terms, Computing the CEV option pricing formula using the semiclassical approximation of path integral, Nonlinear climate dynamics: from deterministic behaviour to stochastic excitability and chaos, Stochastic models with multiplicative noise for economic inequality and mobility, Effects of a fluctuating carrying capacity on the generalized Malthus-Verhulst model, Adaptive learning in large populations, Fractional Brownian motions via random walk in the complex plane and via fractional derivative. Comparison and further results on their Fokker-Planck equations, Hofstadter spectrum in electric and magnetic fields, Kullback-Leibler divergence and mutual information of experiments in the fuzzy case, A nonlinear model for DNA dynamics, Hamilton-Jacobi and Fokker-Planck equations for the harmonic oscillator, Analysis of transport properties determined by Langevin dynamics using Green-Kubo formulae, Stochastic approaches to Lagrangian coherent structures, A new approach to complex-valued fractional Brownian motion via rotating white noise, A predictor-corrector scheme for solving the time fractional Fokker-Planck equation with uniform and non-uniform meshes, Mechanics of biomolecules, Analytical solution in Laplace domain of Smoluchowski equation for a flat potential with a rectangular sink, Broken detailed balance and non-equilibrium dynamics in noisy social learning models, Mapping input noise to escape noise in integrate-and-fire neurons: a level-crossing approach, Stochastic calculus in physics, Combination of transition probability distribution and stable Lorentz distribution in stock markets, Deep relaxation: partial differential equations for optimizing deep neural networks, A quasi birth-and-death model for tumor recurrence, Colored-noise-induced parametric resonance, Meshless local Petrov-Galerkin method for 2D fractional Fokker-Planck equation involved with the ABC fractional derivative, Diffusion and memory effect in a stochastic process and the correspondence to an information propagation in a social system, Violation of the second law of thermodynamics in the quantum microworld, Anomalous diffusion, nonlinear fractional Fokker-Planck equation and solutions, On the periodic Wigner--Poisson--Fokker--Planck system, Fractional (space-time) Fokker-Planck equation, A trajectorial approach to relative entropy dissipation of McKean-Vlasov diffusions: gradient flows and HWBI inequalities, Operator formalism for topology-conserving crossing dynamics in planar knot diagrams, Random time-dependent Brownian motion a new approach to fractals of order \(n\), Signal amplification factor in stochastic resonance: an analytic non-perturbative approach, Velocity Integration in a Multilayer Neural Field Model of Spatial Working Memory, Local Existence for the Dumbbell Model of Polymeric Fluids, Reducing mean first passage times with intermittent confining potentials: a realization of resetting processes, Classical Markovian kinetic equations: Explicit form andH-theorem, Anomalous dispersion in chemically heterogeneous media induced by long-range disorder correlation, Brownian Motion in the Fluids with Complex Rheology, Generalization of Stokes–Einstein relation to coordinate dependent damping and diffusivity: an apparent conflict, The Wigner-Poisson-Fokker-Planck system: global-in-time solution and dispersive effects, Unnamed Item, Stochastic modelling of non-stationary financial assets, Dynamical properties of generalized traveling waves of exactly solvable forced Burgers equations with variable coefficients, Nonlinear Fokker–Planck equation exhibiting bifurcation phenomena and generalized thermostatistics, Unnamed Item, Stochastic Generation and Deformation of Toroidal Oscillations in Neuron Model, Tracking control of non-linear stochastic systems by using path cross-entropy and Fokker-Planck equation, Multiple current reversals and diffusion enhancement in a symmetrical periodic potential, On universal features of the turbulent cascade in terms of non-equilibrium thermodynamics, Checking the Validity of Truncating the Cumulant Hierarchy Description of a Small System, Entropic Regularization of NonGradient Systems, Decision Dynamics in Groups with Interacting Members, A study of Michaelis-Menten type harvesting effects on a population in stochastic environment, Quantifying acoustic damping using flame chemiluminescence, Detailed balance in non-equilibrium systems, Observation time dependent mean first passage time of diffusion and subdiffusion processes, A MONTE CARLO ASSISTED SIMULATION OF STOCHASTIC MOLECULAR DYNAMICS FOR FOLDING OF THE PROTEIN CRAMBIN IN A VISCOUS ENVIRONMENT, φ-Entropies: convexity, coercivity and hypocoercivity for Fokker–Planck and kinetic Fokker–Planck equations, Suppression of viscosity enhancement around a Brownian particle in a near-critical binary fluid mixture, Effect of spatial correlation on stochastic resonance in two linearly interacting noisy bistable oscillators, Joint probability distributions and fluctuation theorems, Gallavotti-Cohen theorem, chaotic hypothesis and the zero-noise limit, Large lattice fractional Fokker–Planck equation, Linear stochastic thermodynamics for periodically driven systems, Suppression of thermal noise in a non-Markovian random velocity field, Analysis of slow transitions between nonequilibrium steady states, Modeling of epidemic spreading on multilayer networks in uncertain environments, Generalized low-energy expansion formula for Green’s function of the Fokker–Planck equation, THE INFLUENCE OF INDIVIDUAL DRIVER CHARACTERISTICS ON CONGESTION FORMATION, Second-Order Schemes for Fokker-Planck Equations with Discontinuous Drift, Monte carlo evaluation of functionals of solutions of stochastic differential equations. variance reduction and numerical examples, Fractional Fokker-Planck equation, Robust identification of harmonic oscillator parameters using the adjoint Fokker–Planck equation, On a class of multitime evolution equations with nonlocal initial conditions, Approximation of the Mean Escape Time for a Tilted Periodic Potential, Diffusion coefficient of a Brownian particle with a friction function given by a power law, Fokker-Planck dynamics of forest systems, Probabilistic structural dynamics of protein folding, Physics and social science -- the approach of synergetics, Stationary properties in a single-mode laser with cross-correlation between quantum noise terms, Effect of colored noise on an overdamped Josephson junction, Local diffusion models for stochastic reacting systems: estimation issues in equation-free numerics, Noises-induced toggle switch and stability in a gene regulation network, Effects of colored noise on the intensity and phase in a laser system, Ratchet, pawl and spring Brownian motor, Evidence of Markov properties of high frequency exchange rate data, Thin-film flow influenced by thermal noise, On using random walks to solve the space-fractional advection-dispersion equations, Towards an approach to stochastic adaptive control using the maximum entropy principle, On the determination of nonlinear response distributions for oscillators with combined harmonic and random excitation, Large-eddy simulation of particle-laden turbulent flows, Linear response and correlation of a self-propelled particle in the presence of external fields, Turbulent mass inhomogeneities induced by a point-source, Unresolved computation and optimal predictions, First Passage Time Memory Lifetimes for Simple, Multistate Synapses: Beyond the Eigenvector Requirement, Barriers to the Transport of Diffusive Scalars in Compressible Flows, Time-dependent Kramers escape rate in overdamped system with power-law distribution, Second-law-like inequalities with information and their interpretations, Quasi-stationary states of game-driven systems: A dynamical approach, Mean first passage time for a class of non-Markovian processes, A Gaussian graphical model approach to climate networks, Stochastic Dynamics of Logistic Tumor Growth, Nonlocal Approximations to Fokker-Planck Equations, Conservative random walks in confining potentials, Characterising the nonequilibrium stationary states of Ornstein–Uhlenbeck processes, Estimation of Critical Conditions for Noise-Induced Bifurcation in Nonautonomous Nonlinear Systems by Stochastic Sensitivity Function, Undiased monte carlo estimators for functionals of weak solutions of stochastic diffretial equations, Stationary probability density of stochastic search processes in global optimization, The probability distribution of returns in the exponential Ornstein–Uhlenbeck model, How irreversible are steady-state trajectories of a trapped active particle?, Local time of an Ornstein–Uhlenbeck particle, Analysis of moment stability and sensitivity of non-linear stochastic distributed systems: a practical approach via a distributed Fokker-Planck equation, Fokker–Planck representations of non-Markov Langevin equations: application to delayed systems, Exact Universal Excitation Waveform for Optimal Enhancement of Directed Ratchet Transport, Hitting-Time Densities of a Two-Dimensional Markov Process, Linear response characteristics in time-dependent subdiffusive fractional Fokker–Planck equations, The stochastic logistic equation: stationary solutions and their stability, Quantum optimal control using the adjoint method, Formulation of a unified method for low- and high-energy expansions in the analysis of reflection coefficients for one-dimensional Schrödinger equation, Relating the thermodynamic arrow of time to the causal arrow, Option pricing under stochastic volatility: the exponential Ornstein–Uhlenbeck model, Multiplicative Langevin equation to reproduce long-time properties of nonequilibrium Brownian motion, Intermittent resetting potentials, Notes about the macroscopic fluctuating theory, Charge transport along phenylenevinylene molecular wires, Kinetic equations for classical and quantum Brownian particles and eigenfunction expansions as generalized functions, Statistical nature of infrared dynamics on de Sitter background, Primordial black holes from inflation and quantum diffusion, Stochastic baryogenesis, Optimal response to non-equilibrium disturbances under truncated Burgers–Hopf dynamics, Semi-classical Lindblad master equation for spin dynamics, Brownian motion under intermittent harmonic potentials, Multiple-relaxation-time lattice Boltzmann scheme for fractional advection-diffusion equation, Non-perturbative analysis for a massless minimal quantum scalar with V(ϕ) = λϕ 4/4! + βϕ 3/3! in the inflationary de Sitter spacetime, Transport in a stochastic double diffusivity model, One-dimensional run-and-tumble motions with generic boundary conditions, Cosh gradient systems and tilting, Derivation of wealth distributions from biased exchange of money, Tracking hematopoietic stem cell evolution in a Wiskott-Aldrich clinical trial, Path integral approach via Laplace's method of integration for nonstationary response of nonlinear systems, Stochastic dynamics of nonlinear tumor-immune system with chemotherapy, Succinct description and efficient simulation of non-Markovian open quantum systems, Deriving a kinetic uncertainty relation for piecewise deterministic processes: from classical to quantum, The steady state and response to a periodic stimulation of the firing rate for a theta neuron with correlated noise, Temperature-Frequency Controlling the Characteristics of a Pulsating Brownian Ratchet with Slightly Fluctuating Potential Energy, Net transport and stochastic resonance in an underdamped system due to the application of a traveling-wave force-field, Unnamed Item, Unnamed Item, Hypersensitive transport in a phase model with multiplicative stimulus, New results on Fokker-Planck equations of fractional order., Brownian motors: noisy transport far from equilibrium