Langevin picture of subdiffusion with infinitely divisible waiting times

DOI10.1007/s10955-009-9751-zzbMath1177.82101OpenAlexW2128623506MaRDI QIDQ2390967

Marcin Magdziarz

Publication date: 10 August 2009

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10955-009-9751-z

zbMATH Keywords

infinitely divisible distributionanomalous diffusionfractional Fokker-Planck equationinverse subordinatorsubdiffusionfirst-passage timenon-Markovian dynamicscontinuous time random walksLangevin representation

Mathematics Subject Classification ID

Infinitely divisible distributions; stable distributions (60E07) Central limit and other weak theorems (60F05) Integral transforms in distribution spaces (46F12) Fractional derivatives and integrals (26A33) Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31) Transport processes in time-dependent statistical mechanics (82C70) Processes in random environments (60K37) Numerical solutions to stochastic differential and integral equations (65C30) Stable stochastic processes (60G52)

Related Items (40)

Anomalous diffusion in nonhomogeneous media: power spectral density of signals generated by time-subordinated nonlinear Langevin equations ⋮ Explicit form of the first-passage-time density for accelerating subdiffusion ⋮ Fractional Brownian motion time-changed by gamma and inverse gamma process ⋮ Stochastic solution of fractional Fokker-Planck equations with space-time-dependent coefficients ⋮ Black-Scholes formula in subdiffusive regime ⋮ Strong approximation of stochastic differential equations driven by a time-changed Brownian motion with time-space-dependent coefficients ⋮ From particles scale to anomalous or classical convection-diffusion models with path integrals ⋮ Asymptotic properties of Brownian motion delayed by inverse subordinators ⋮ Langevin picture of subdiffusive particles under the joint influence of an expanding medium and an external constant force ⋮ Modified cumulative distribution function in application to waiting time analysis in the continuous time random walk scenario ⋮ Langevin picture of Lévy walks and their extensions ⋮ Geometric Brownian motion with tempered stable waiting times ⋮ Option pricing in subdiffusive Bachelier model ⋮ Large deviations for subordinated Brownian motion and applications ⋮ Correlated continuous-time random walks—scaling limits and Langevin picture ⋮ The tempered stable process with infinitely divisible inverse subordinators ⋮ Rotational invariance of stochastic processes with application to fractional dynamics ⋮ The subordinated processes controlled by a family of subordinators and corresponding Fokker–Planck type equations ⋮ Fractional Brownian motion delayed by tempered and inverse tempered stable subordinators ⋮ Comment on fractional Fokker-Planck equation with space and time dependent drift and diffusion ⋮ Parameter estimation for one-sided heavy-tailed distributions ⋮ Calibration of the subdiffusive arithmetic Brownian motion with tempered stable waiting-times ⋮ Relaxation patterns and semi-Markov dynamics ⋮ Subdiffusive fractional Black–Scholes model for pricing currency options under transaction costs ⋮ Fokker-Planck type equations associated with fractional Brownian motion controlled by infinitely divisible processes ⋮ Pricing european option under the time-changed mixed Brownian-fractional Brownian model ⋮ Stochastic representation of a fractional subdiffusion equation. The case of infinitely divisible waiting times, Lévy noise and space-time-dependent coefficients ⋮ Duality of fractional systems ⋮ Modeling anomalous diffusion by a subordinated integrated Brownian motion ⋮ Equivalence of subordinated processes with tempered \(\alpha\)-stable waiting times and fractional Fokker-Planck equations in space and time dependent fields ⋮ Diffusion and Fokker-Planck-Smoluchowski equations with generalized memory kernel ⋮ Strong approximation of time-changed stochastic differential equations involving drifts with random and non-random integrators ⋮ Fokker-Planck equation for a metastable time dependent potential ⋮ Characterizing anomalous diffusion by studying displacements ⋮ Moment-based estimation for parameters of general inverse subordinator ⋮ Models for characterizing the transition among anomalous diffusions with different diffusion exponents ⋮ Time-averaged mean squared displacement ratio test for Gaussian processes with unknown diffusion coefficient ⋮ Feynman–Kac equation for anomalous processes with space- and time-dependent forces ⋮ Empirical anomaly measure for finite-variance processes ⋮ Confined random motion with Laplace and Linnik statistics

Cites Work

• Unnamed Item
• Unnamed Item
• Stochastic representation of subdiffusion processes with time-dependent drift
• Doubly stochastic Poisson processes
• Can one see \(\alpha\)-stable variables and processes?
• Renewal theory and level passage by subordinators
• Lévy-driven Langevin systems: targeted stochasticity
• On the Chambers-Mallows-Stuck method for simulating skewed stable random variables
• Two-time scale subordination in physical processes with long-term memory
• Stochastic model for ultraslow diffusion
• STATIONARITY OF DELAYED SUBORDINATORS
• Stochastic solution of space-time fractional diffusion equations
• Random Walks on Lattices. II
• An Introduction to the Theory of Point Processes
• Electronic Foreign-Exchange Markets and Passage Events of Independent Subordinators
• A renewal-process-type expression for the moments of inverse subordinators
• The random walk's guide to anomalous diffusion: A fractional dynamics approach

This page was built for publication: Langevin picture of subdiffusion with infinitely divisible waiting times