Second order PDE's in finite and infinite dimension
From MaRDI portal
Publication:5937522
DOI10.1007/b80743zbMath0983.60004OpenAlexW2506637745MaRDI QIDQ5937522
Publication date: 12 July 2001
Published in: Lecture Notes in Mathematics (Search for Journal in Brave)
Full work available at URL: http://link.springer.de/link/service/series/0304/tocs/t1762.htm
stochastic differential equationsstochastic partial differential equationsBismut-Elworthy formulaKolmogorov equationssecond order parabolic equations
Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Dynamic programming in optimal control and differential games (49L20) Second-order elliptic equations (35J15) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Initial value problems for second-order parabolic equations (35K15) PDEs on infinite-dimensional (e.g., function) spaces (= PDEs in infinitely many variables) (35R15) Research exposition (monographs, survey articles) pertaining to probability theory (60-02)
Related Items
Approximation of the invariant distribution for a class of ergodic SPDEs using an explicit tamed exponential Euler scheme ⋮ A new criterion on existence and uniqueness of stationary distribution for diffusion processes ⋮ Path-Dependent SDEs in Hilbert Spaces ⋮ Existence and uniqueness of global solutions to the stochastic heat equation with superlinear drift on an unbounded spatial domain ⋮ Stochastic Control Problems with Unbounded Control Operators: Solutions Through Generalized Derivatives ⋮ A Probabilistic Approach to Classical Solutions of the Master Equation for Large Population Equilibria ⋮ Large Deviations for Semilinear Differential Stochastic Equations with Dissipative Non-linearities ⋮ Sufficient conditions for optimality for stochastic evolution equations ⋮ On Asymptotic Preserving Schemes for a Class of Stochastic Differential Equations in Averaging and Diffusion Approximation Regimes ⋮ A Khasminskii type averaging principle for stochastic reaction-diffusion equations ⋮ Singular stochastic equations on Hilbert spaces: Harnack inequalities for their transition semigroups ⋮ Coupling by reflection and Hölder regularity for non-local operators of variable order ⋮ An integral inequality for the invariant measure of a stochastic reaction-diffusion equation ⋮ Invariant measures for stochastic reaction–diffusion equations with weakly dissipative nonlinearities ⋮ A priori bounds for rough differential equations with a non-linear damping term ⋮ Robust control of parabolic stochastic partial differential equations under model uncertainty ⋮ Rate of homogenization for fully-coupled McKean–Vlasov SDEs ⋮ Splitting integrators for stochastic Lie–Poisson systems ⋮ Time regularity for generalized Mehler semigroups ⋮ On the Lie-Trotter approximation formula ⋮ \(L^2\)-theory for transition semigroups associated to dissipative systems ⋮ Splitting schemes for FitzHugh-Nagumo stochastic partial differential equations ⋮ Ergodic maximum principle for stochastic systems ⋮ Near-optimal control of a stochastic partial differential equation SEIR epidemic model under economic constraints ⋮ Ergodicity of supercritical SDEs driven by \(\alpha \)-stable processes and heavy-tailed sampling ⋮ Regularizing properties of (non-Gaussian) transition semigroups in Hilbert spaces ⋮ Weak variable step-size schemes for stochastic differential equations based on controlling conditional moments ⋮ Well-posedness and stationary solutions of McKean-Vlasov (S)PDEs ⋮ Global dynamics of a stochastic reaction–diffusion predator–prey system with space-time white noise ⋮ Moderate deviations for systems of slow-fast stochastic reaction-diffusion equations ⋮ Schauder regularity results in separable Hilbert spaces ⋮ Necessary stochastic maximum principle for dissipative systems on infinite time horizon ⋮ Approximation of the invariant distribution for a class of ergodic SDEs with one-sided Lipschitz continuous drift coefficient using an explicit tamed Euler scheme ⋮ Effective splitting of invariant measures for a stochastic reaction diffusion equation with multiplicative noise ⋮ Stochastic Optimal Control for the Stochastic Heat Equation with Exponentially Growing Coefficients and with Control and Noise on a Subdomain ⋮ Exponential ergodicity for non-Lipschitz multivalued stochastic differential equations with Lévy jumps ⋮ Bismut-Elworthy-Li Formulae for Bessel Processes ⋮ Invariant measures for monotone SPDEs with multiplicative noise term ⋮ Continuous-time Random Walks for the Numerical Solution of Stochastic Differential Equations ⋮ Asymptotic analysis and homogenization of invariant measures ⋮ Conservative stochastic Cahn-Hilliard equation with reflection ⋮ Analysis of a spatially inhomogeneous stochastic partial differential equation epidemic model ⋮ Elliptic and Parabolic Second-Order PDEs with Growing Coefficients ⋮ Unnamed Item ⋮ A Random String with Reflection in a Convex Domain ⋮ On the Exponential Ergodicity of Lévy-Driven Ornstein–Uhlenbeck Processes ⋮ SPECTRWM: Spectral Random Walk Method for the Numerical Solution of Stochastic Partial Differential Equations ⋮ Malliavin calculus for non-Gaussian differentiable measures and surface measures in Hilbert spaces ⋮ On a class of forward-backward stochastic differential systems in infinite dimensions ⋮ Optimal Investment Under Information Driven Contagious Distress ⋮ Estimates of the derivatives for parabolic operators with unbounded coefficients ⋮ Infinite dimensional stochastic differential equations of Ornstein-Uhlenbeck type ⋮ On basin of zero-solutions to a semilinear parabolic equation with Ornstein-Uhlenbeck operator ⋮ Hypercontractivity and Asymptotic Behavior in Nonautonomous Kolmogorov Equations ⋮ Dirichlet boundary conditions for elliptic operators with unbounded drift ⋮ Gradient estimates for diffusion semigroups with singular coefficients ⋮ Kolmogorov equations in infinite dimensions: well-posedness and regularity of solutions, with applications to stochastic generalized Burgers equations ⋮ Metastable behaviour of small noise Lévy-Driven diffusions ⋮ Backward stochastic partial differential equations driven by infinite-dimensional martingales and applications ⋮ Exponential ergodicity of non-Lipschitz stochastic differential equations ⋮ Asymptotic behaviour of stochastic quasi dissipative systems ⋮ Stochastic Maximum Principle for Optimal Control of a Class of Nonlinear SPDEs with Dissipative Drift ⋮ Approximation of quasi-potentials and exit problems for multidimensional RDE’s with noise ⋮ Exponential ergodicity for non-Lipschitz white noise driven parabolic stochastic partial differential equations with two reflecting walls ⋮ Restoring uniqueness to mean-field games by randomizing the equilibria ⋮ Stochastic homogenization of multicontinuum heterogeneous flows ⋮ Averaging Principle for Nonautonomous Slow-Fast Systems of Stochastic Reaction-Diffusion Equations: The Almost Periodic Case ⋮ Calculus via regularizations in Banach spaces and Kolmogorov-type path-dependent equations ⋮ Multivariate approximations in Wasserstein distance by Stein's method and Bismut's formula ⋮ STOCHASTIC CAHN–HILLIARD PARTIAL DIFFERENTIAL EQUATIONS WITH LÉVY SPACETIME WHITE NOISES ⋮ Space-Time Regularity of Solutions of the Parabolic Stochastic Cauchy Problem ⋮ A mild Itô formula for SPDEs ⋮ Large deviations for the dynamic \(\phi ^{2n}_d\) model ⋮ On a Class of Stochastic Semilinear PDEs ⋮ Stochastic Homogenization of a Convection-Diffusion Equation ⋮ Gradient estimates for perturbed Ornstein-Uhlenbeck semigroups on infinite-dimensional convex domains ⋮ Stabilization by noise for a class of stochastic reaction-diffusion equations ⋮ Nonlinear Young integrals and differential systems in Hölder media ⋮ Itô's- and Tanaka's-type formulae for the stochastic heat equation: The linear case ⋮ Invariant measures for stochastic heat equations with unbounded coefficients. ⋮ Loss of regularity for Kolmogorov equations ⋮ Schauder theorems for a class of (pseudo‐)differential operators on finite‐ and infinite‐dimensional state spaces ⋮ A note on the strong maximum principle ⋮ Integration by parts on \(\delta\)-Bessel bridges, \(\delta>3\), and related SPDEs ⋮ Homogenization for stochastic reaction-diffusion equations with singular perturbation term ⋮ A new approach to Kolmogorov equations in infinite dimensions and applications to stochastic generalized Burgers equations ⋮ Euclidean Gibbs measures on loop lattices: existence and a priori estimates. ⋮ Infinite horizon backward stochastic differential equations and elliptic equations in Hilbert spaces. ⋮ Large deviations for stochastic reaction-diffusion systems with multiplicative noise and non-Lipschitz reaction term. ⋮ Homogenization of Brinkman flows in heterogeneous dynamic media ⋮ BV functions in Hilbert spaces ⋮ On backward Kolmogorov equation related to CIR process ⋮ Lower estimates of transition densities and bounds on exponential ergodicity for stochastic PDEs ⋮ Existence and uniqueness of invariant measures for stochastic reaction-diffusion equations in unbounded domains ⋮ A probabilistic formula for gradients of solutions of hypoelliptic Dirichlet problems ⋮ A new topological approach to the \(L^{\infty }\)-uniqueness of operators and the \(L^{1}\)-uniqueness of Fokker--Planck equations ⋮ Essential self-adjointness of Dirichlet operators on a path space with Gibbs measures via an SPDE approach ⋮ Some classes of non-analytic Markov semigroups ⋮ Maximum principles for infinite dimensional diffusion equations ⋮ Existence and regularity of the density for solutions to semilinear dissipative parabolic SPDEs ⋮ Adaptive Galerkin approximation algorithms for Kolmogorov equations in infinite dimensions ⋮ Orders of convergence in the averaging principle for SPDEs: the case of a stochastically forced slow component ⋮ Pathwise uniqueness for stochastic reaction-diffusion equations in Banach spaces with an Hölder drift component ⋮ Local bounds for stochastic reaction diffusion equations ⋮ On a perturbation theory and on strong convergence rates for stochastic ordinary and partial differential equations with nonglobally monotone coefficients ⋮ Spectral analysis for a discrete metastable system driven by Lévy flights ⋮ Asymptotic behavior in time periodic parabolic problems with unbounded coefficients ⋮ A basic identity for Kolmogorov operators in the space of continuous functions related to RDEs with multiplicative noise ⋮ A nonlinear Bismut-Elworthy formula for HJB equations with quadratic Hamiltonian in Banach spaces ⋮ Weak convergence rates of splitting schemes for the stochastic Allen-Cahn equation ⋮ A full-discrete exponential Euler approximation of the invariant measure for parabolic stochastic partial differential equations ⋮ Fréchet differentiability of mild solutions to SPDEs with respect to the initial datum ⋮ An efficient explicit full-discrete scheme for strong approximation of stochastic Allen-Cahn equation ⋮ On Wiener-Poisson type multivalued stochastic differential equations with non-Lipschitz coefficients ⋮ Strong and weak orders in averaging for SPDEs ⋮ Schauder estimates for elliptic equations in Banach spaces associated with stochastic reaction-diffusion equations ⋮ Average and deviation for slow-fast stochastic partial differential equations ⋮ A numerical approach to Kolmogorov equation in high dimension based on Gaussian analysis ⋮ Ornstein-Uhlenbeck processes with singular drifts: integral estimates and Girsanov densities ⋮ Large deviations for invariant measures of general stochastic reaction-diffusion systems ⋮ Exponential ergodicity for SDEs with jumps and non-Lipschitz coefficients ⋮ A skew stochastic heat equation ⋮ \(C_0\)-sequentially equicontinuous semigroups ⋮ Jump type stochastic differential equations with non-Lipschitz coefficients: non-confluence, Feller and strong Feller properties, and exponential ergodicity ⋮ Differentiability of SDEs with drifts of super-linear growth ⋮ Elliptic operators with unbounded drift coefficients and Neumann boundary condition. ⋮ On regularity of invariant measures of multivalued stochastic differential equations ⋮ Ergodicity of linear SPDE driven by Lévy noise ⋮ Robust control and hot spots in spatiotemporal economic systems ⋮ Regularity properties for solutions of infinite dimensional Kolmogorov equations in Hilbert spaces ⋮ A brief and personal history of stochastic partial differential equations ⋮ Ergodic and mixing properties of the Boussinesq equations with a degenerate random forcing ⋮ A semi-linear backward parabolic Cauchy problem with unbounded coefficients of Hamilton-Jacobi-Bellman type and applications to optimal control ⋮ On the Smoluchowski-Kramers approximation for SPDEs and its interplay with large deviations and long time behavior ⋮ Systems of small-noise stochastic reaction-diffusion equations satisfy a large deviations principle that is uniform over all initial data ⋮ Importance sampling in path space for diffusion processes with slow-fast variables ⋮ Gradient estimates for SDEs without monotonicity type conditions ⋮ Strong convergence rates for nonlinearity-truncated Euler-type approximations of stochastic Ginzburg-Landau equations ⋮ Strong-viscosity solutions: classical and path-dependent PDEs ⋮ Necessary conditions for optimal control of stochastic evolution equations in Hilbert spaces ⋮ \(L^p\)-regularity for parabolic operators with unbounded time-dependent coefficients ⋮ Gradient estimates for Dirichlet parabolic problems in unbounded domains ⋮ Liouville theorems for non-local operators ⋮ Exponential ergodicity of non-Lipschitz multivalued stochastic differential equations ⋮ Flow of diffeomorphisms for SDEs with unbounded Hölder continuous drift ⋮ Necessary conditions for optimality for stochastic evolution equations ⋮ Variational solutions of dissipative jump-type stochastic evolution equations ⋮ A Bismut-Elworthy formula for quadratic BSDEs ⋮ Schauder theorems for Ornstein-Uhlenbeck equations in infinite dimension ⋮ Improved moment estimates for invariant measures of semilinear diffusions in Hilbert spaces and applications ⋮ Weak convergence and invariant measure of a full discretization for parabolic SPDEs with non-globally Lipschitz coefficients ⋮ Stochastic partial differential equation models for spatially dependent predator-prey equations ⋮ Weak convergence rates for an explicit full-discretization of stochastic Allen-Cahn equation with additive noise ⋮ Kolmogorov equations and weak order analysis for SPDEs with nonlinear diffusion coefficient ⋮ Mild solutions of semilinear elliptic equations in Hilbert spaces ⋮ Measuring sample quality with diffusions ⋮ Ergodicity and Kolmogorov equations for dissipative SPDEs with singular drift: a variational approach ⋮ Uniqueness of solutions to degenerate elliptic problems with unbounded coefficients ⋮ Fokker-Planck equations and maximal dissipativity for Kolmogorov operators with time dependent singular drifts in Hilbert spaces ⋮ Invariant measures for stochastic evolution equations of pure jump type ⋮ On the convergence of stationary solutions in the Smoluchowski-Kramers approximation of infinite dimensional systems ⋮ Drift estimation for stochastic reaction-diffusion systems ⋮ Invariant measures and asymptotic Gaussian bounds for normal forms of stochastic climate model ⋮ Existence of mild solutions for stochastic differential equations and semilinear equations with non-Gaussian Lévy noise ⋮ Emergence of oscillatory behaviors for excitable systems with noise and mean-field interaction: a slow-fast dynamics approach ⋮ Mean field limit for disordered diffusions with singular interactions ⋮ Cores for parabolic operators with unbounded coefficients ⋮ Averaging principle for a class of stochastic reaction-diffusion equations ⋮ An adaptive time-stepping method based on a posteriori weak error analysis for large SDE systems ⋮ On Feller and strong Feller properties and irreducibility of regime-switching jump diffusion processes with countable regimes ⋮ Maximal dissipativity of Kolmogorov operators with Cahn--Hilliard type drift term ⋮ On generators of transition semigroups associated to semilinear stochastic partial differential equations ⋮ Stochastic reaction-diffusion equations on networks ⋮ Deterministic control of stochastic reaction-diffusion equations ⋮ Global solutions for the stochastic reaction-diffusion equation with super-linear multiplicative noise and strong dissipativity ⋮ Ruelle-Pollicott resonances of stochastic systems in reduced state space. Part I: Theory ⋮ Ruelle-Pollicott resonances of stochastic systems in reduced state space. Part II: Stochastic Hopf bifurcation ⋮ Ruelle-Pollicott resonances of stochastic systems in reduced state space. Part III: Application to the Cane-Zebiak model of the El Niño-southern oscillation ⋮ Risk-sensitive credit portfolio optimization under partial information and contagion risk ⋮ Regular dependence on initial data for stochastic evolution equations with multiplicative Poisson noise ⋮ A Bismut-Elworthy inequality for a Wasserstein diffusion on the circle ⋮ Harnack inequalities with power \(\pmb{p\in (1,+\infty )}\) for transition semigroups in Hilbert spaces ⋮ Ergodicity of a nonlinear stochastic reaction-diffusion equation with memory
