A note on the asymptotic stability of the semi-discrete method for stochastic differential equations

DOI10.1515/MCMA-2022-2102zbMath1492.60170arXiv2008.03148OpenAlexW3048027821WikidataQ115235975 ScholiaQ115235975MaRDI QIDQ2121623

Ioannis S. Stamatiou, Nikolaos Halidias

Publication date: 4 April 2022

Published in: Monte Carlo Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2008.03148

zbMATH Keywords

asymptotic stabilitysemi-discrete methodexplicit numerical schemenon-linear stochastic differential equations

Mathematics Subject Classification ID

Probabilistic models, generic numerical methods in probability and statistics (65C20) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical solutions to equations with nonlinear operators (65J15) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30)

Cites Work

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• An explicit positivity preserving numerical scheme for CIR/CEV type delay models with jump
• A boundary preserving numerical scheme for the Wright-Fisher model
• A novel approach to construct numerical methods for stochastic differential equations
• Strong and weak divergence in finite time of Euler's method for stochastic differential equations with non-globally Lipschitz continuous coefficients
• Convergence rates of the Semi-Discrete method for stochastic differential equations
• Semi-discrete approximations for stochastic differential equations and applications

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