Stochastic Averaging of Dynamical Systems with Multiple Time Scales Forced with $\alpha$-Stable Noise

DOI10.1137/140990632zbMath1333.34099arXiv1410.1837OpenAlexW2098364017MaRDI QIDQ3459652

Adam Hugh Monahan, William F. Thompson, Rachel Kuske

Publication date: 11 January 2016

Published in: Multiscale Modeling & Simulation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1410.1837

zbMATH Keywords

Lévy processesstochastic differential equationsnumerical simulationmultiple time scalesstochastic averagingalpha-stable processesheavy-tailed processesMarcus calculus

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Averaging method for ordinary differential equations (34C29) Ordinary differential equations and systems with randomness (34F05) Numerical solutions to stochastic differential and integral equations (65C30) Stable stochastic processes (60G52) Multiple scale methods for ordinary differential equations (34E13)

Related Items (13)

Two-time-scales hyperbolic-parabolic equations driven by Poisson random measures: existence, uniqueness and averaging principles ⋮ Reduced α-stable dynamics for multiple time scale systems forced with correlated additive and multiplicative Gaussian white noise ⋮ Type II Singular Perturbation Approximation for Linear Systems with Lévy Noise ⋮ The averaging method for doubly perturbed distribution dependent SDEs ⋮ Singular perturbation approximation for linear systems with Lévy noise ⋮ Averaging principles for mixed fast-slow systems driven by fractional Brownian motion ⋮ Averaging principles for nonautonomous two-time-scale stochastic reaction-diffusion equations with jump ⋮ Stochastic averaging for two-time-scale stochastic partial differential equations with fractional Brownian motion ⋮ Stochastic averaging for a class of two-time-scale systems of stochastic partial differential equations ⋮ Stochastic averaging principles for multi-valued stochastic differential equations driven by poisson point Processes ⋮ Convergence of \(p\)-th mean in an averaging principle for stochastic partial differential equations driven by fractional Brownian motion ⋮ Two-time-scale stochastic differential delay equations driven by multiplicative fractional Brownian noise: averaging principle ⋮ A new type of singular perturbation approximation for stochastic bilinear systems

Uses Software

• Matlab
• STABLE

Cites Work

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