Convergence rate and stability of the split-step theta method for stochastic differential equations with piecewise continuous arguments

DOI10.3934/dcdsb.2018203zbMath1404.65073OpenAlexW2809233765WikidataQ129415908 ScholiaQ129415908MaRDI QIDQ1755935

Minghui Song, Yulan Lu, Ming-Zhu Liu

Publication date: 11 January 2019

Published in: Discrete and Continuous Dynamical Systems. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcdsb.2018203

zbMATH Keywords

convergence rateexponential mean square stabilitystochastic differential equations with piecewise continuous argumentsthe improved split-step theta (ISST) methodthe split-step theta (SST) method

Mathematics Subject Classification ID

Probabilistic models, generic numerical methods in probability and statistics (65C20) Stability and convergence of numerical methods for ordinary differential equations (65L20) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35)

Related Items

The Convergence of Truncated Euler-Maruyama Method for Stochastic Differential Equations with Piecewise Continuous Arguments Under Generalized One-Sided Lipschitz Condition ⋮ Numerical solution of stochastic state-dependent delay differential equations: convergence and stability ⋮ Convergence and stability of the Milstein scheme for stochastic differential equations with piecewise continuous arguments ⋮ Stability equivalence among stochastic differential equations and stochastic differential equations with piecewise continuous arguments and corresponding Euler-Maruyama methods ⋮ Stochastic differential equation with piecewise continuous arguments: Markov property, invariant measure and numerical approximation

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