Simulation of Non-Lipschitz Stochastic Differential Equations Driven by $\alpha$-Stable Noise: A Method Based on Deterministic Homogenization

DOI10.1137/20M1333183zbMath1470.60200arXiv2004.09914OpenAlexW3153804399WikidataQ115246899 ScholiaQ115246899MaRDI QIDQ4992254

Georg A. Gottwald, Ian Melbourne

Publication date: 8 June 2021

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

Full work available at URL: https://arxiv.org/abs/2004.09914

zbMATH Keywords

Lévy processeshomogenizationstable lawsmultiscale dynamicsnumerical simulation of SDEs

Mathematics Subject Classification ID

Dynamical systems and their relations with probability theory and stochastic processes (37A50) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Functional limit theorems; invariance principles (60F17)

Uses Software

• Matlab

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Smooth approximation of stochastic differential equations
• Euler approximations with varying coefficients: the case of superlinearly growing diffusion coefficients
• Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficients
• On tamed Milstein schemes of SDEs driven by Lévy noise
• A note on tamed Euler approximations
• Transformations on [0,1 with infinite invariant measures]
• Convergence rates of the truncated Euler-Maruyama method for stochastic differential equations
• Chaotic advection in a two-dimensional flow: Lévy flights and anomalous diffusion
• Estimates of the invariant densities of endomorphisms with indifferent fixed points
• Recurrence times and rates of mixing
• Subexponential decay of correlations
• Central limit theorem and stable laws for intermittent maps
• Canonical RDEs and general semimartingales as rough paths
• Statistical limit theorems for suspension flows
• Sharp polynomial estimates for the decay of correlations
• On a perturbation theory and on strong convergence rates for stochastic ordinary and partial differential equations with nonglobally monotone coefficients
• Stochastic differential calculus for Gaussian and non-Gaussian noises: a critical review
• Superdiffusive limits for deterministic fast-slow dynamical systems
• On a positivity preserving numerical scheme for jump-extended CIR process: the alpha-stable case
• Molecular dynamics. With deterministic and stochastic numerical methods
• Weak convergence to stable Lévy processes for nonuniformly hyperbolic dynamical systems
• Mixing limit theorems for ergodic transformations
• Stochastic simulation: Algorithms and analysis
• Continuous Markov processes and stochastic equations
• Approximations of small jumps of Lévy processes with a view towards simulation
• Stochastic-Process Limits
• On Tamed Euler Approximations of SDEs Driven by Lévy Noise with Applications to Delay Equations
• Numerical approximations of stochastic differential equations with non-globally Lipschitz continuous coefficients
• Strong and weak divergence in finite time of Euler's method for stochastic differential equations with non-globally Lipschitz continuous coefficients
• Marcus versus Stratonovich for systems with jump noise
• Statistical properties of a skew product with a curve of neutral points
• WEAK CONVERGENCE TO LÉVY STABLE PROCESSES IN DYNAMICAL SYSTEMS
• Lévy Processes and Stochastic Calculus
• Two-sided bounds on the rate of convergence to a stable law
• Modeling and approximation of stochastic differential equations driven by semimartingales^†
• A Method for Simulating Stable Random Variables
• Some Simple Conditions for Limit Theorems to Be Mixing
• Ergodic Theory for Markov Fibred Systems and Parabolic Rational Maps
• A probabilistic approach to intermittency
• Limit theorems for partially hyperbolic systems
• LOCAL LIMIT THEOREMS FOR PARTIAL SUMS OF STATIONARY SEQUENCES GENERATED BY GIBBS–MARKOV MAPS
• The asymptotics of the Perron-Frobenius operator of a class of interval maps preserving infinite measures
• Adaptive time-stepping strategies for nonlinear stochastic systems
• Extracting macroscopic dynamics: model problems and algorithms
• Decay of correlations for piecewise smooth maps with indifferent fixed points
• Strong Convergence of Euler-Type Methods for Nonlinear Stochastic Differential Equations
• STABLE LIMITS FOR PROBABILITY PRESERVING MAPS WITH INDIFFERENT FIXED POINTS
• Financial Modelling with Jump Processes
• Nonlinear and Stochastic Climate Dynamics
• Homogenization for deterministic maps and multiplicative noise
• A Fundamental Mean-Square Convergence Theorem for SDEs with Locally Lipschitz Coefficients and Its Applications
• Euler scheme for SDEs with non-Lipschitz diffusion coefficient: strong convergence
• Numerical Integration of Stochastic Differential Equations with Nonglobally Lipschitz Coefficients
• Error rates in the Darling–Kac law

This page was built for publication: Simulation of Non-Lipschitz Stochastic Differential Equations Driven by $\alpha$-Stable Noise: A Method Based on Deterministic Homogenization