Numerical method of highly nonlinear and nonautonomous neutral stochastic differential delay equations with Markovian switching

Abstract In this paper, we establish a partially truncated Euler–Maruyama scheme for highly nonlinear and nonautonomous neutral stochastic differential delay equations with Markovian switching. We investigate the strong convergence rate and almost sure exponential stability of the numerical solution...

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Main Authors: Shuaibin Gao, Junhao Hu
Format: Article
Language:English
Published: SpringerOpen 2020-12-01
Series:Advances in Difference Equations
Subjects:
Online Access:https://doi.org/10.1186/s13662-020-03113-x
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author Shuaibin Gao
Junhao Hu
author_facet Shuaibin Gao
Junhao Hu
author_sort Shuaibin Gao
collection DOAJ
description Abstract In this paper, we establish a partially truncated Euler–Maruyama scheme for highly nonlinear and nonautonomous neutral stochastic differential delay equations with Markovian switching. We investigate the strong convergence rate and almost sure exponential stability of the numerical solutions under the generalized Khasminskii-type condition.
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spelling doaj.art-8647f1f5b68d47679b608726c08c1f0d2022-12-21T20:31:52ZengSpringerOpenAdvances in Difference Equations1687-18472020-12-012020113710.1186/s13662-020-03113-xNumerical method of highly nonlinear and nonautonomous neutral stochastic differential delay equations with Markovian switchingShuaibin Gao0Junhao Hu1College of Mathematics and Statistics, South-Central University for NationalitiesCollege of Mathematics and Statistics, South-Central University for NationalitiesAbstract In this paper, we establish a partially truncated Euler–Maruyama scheme for highly nonlinear and nonautonomous neutral stochastic differential delay equations with Markovian switching. We investigate the strong convergence rate and almost sure exponential stability of the numerical solutions under the generalized Khasminskii-type condition.https://doi.org/10.1186/s13662-020-03113-xPartially truncated Euler–Maruyama methodNeutral stochastic differential delay equationsMarkovian switchingHighly nonlinear and nonautonomous equations
spellingShingle Shuaibin Gao
Junhao Hu
Numerical method of highly nonlinear and nonautonomous neutral stochastic differential delay equations with Markovian switching
Advances in Difference Equations
Partially truncated Euler–Maruyama method
Neutral stochastic differential delay equations
Markovian switching
Highly nonlinear and nonautonomous equations
title Numerical method of highly nonlinear and nonautonomous neutral stochastic differential delay equations with Markovian switching
title_full Numerical method of highly nonlinear and nonautonomous neutral stochastic differential delay equations with Markovian switching
title_fullStr Numerical method of highly nonlinear and nonautonomous neutral stochastic differential delay equations with Markovian switching
title_full_unstemmed Numerical method of highly nonlinear and nonautonomous neutral stochastic differential delay equations with Markovian switching
title_short Numerical method of highly nonlinear and nonautonomous neutral stochastic differential delay equations with Markovian switching
title_sort numerical method of highly nonlinear and nonautonomous neutral stochastic differential delay equations with markovian switching
topic Partially truncated Euler–Maruyama method
Neutral stochastic differential delay equations
Markovian switching
Highly nonlinear and nonautonomous equations
url https://doi.org/10.1186/s13662-020-03113-x
work_keys_str_mv AT shuaibingao numericalmethodofhighlynonlinearandnonautonomousneutralstochasticdifferentialdelayequationswithmarkovianswitching
AT junhaohu numericalmethodofhighlynonlinearandnonautonomousneutralstochasticdifferentialdelayequationswithmarkovianswitching