Numerical solutions of regime-switching functional diffusions with infinite delay

We study a class of diffusion processes which are determined by solutions X(t) to stochastic functional differential equation with infinite memory and random switching represented by Markov chain Λ(t). Under suitable conditions, we adopt Euler-Maruyama method to deal with the convergence of numerica...

Full description

Saved in:

Bibliographic Details
Published in:	Stochastic models Vol. 40; no. 4; pp. 617 - 633
Main Authors:	Zhen, Yuhang, Xi, Fubao
Format:	Journal Article
Language:	English
Published:	Philadelphia Taylor & Francis 01-11-2024 Taylor & Francis Ltd
Subjects:	Convergence Differential equations Diffusion rate Lipschitz condition Markov chains rate of convergence regime-switching stochastic functional differential equation
Online Access:	Get full text
Tags:	Add Tag No Tags, Be the first to tag this record!

Description
Summary:	We study a class of diffusion processes which are determined by solutions X(t) to stochastic functional differential equation with infinite memory and random switching represented by Markov chain Λ(t). Under suitable conditions, we adopt Euler-Maruyama method to deal with the convergence of numerical solutions of the corresponding stochastic differential equations. More precisely, we investigate convergence rates in the L 2 -norm the stochastic functional differential equation with infinite memory and random switching under the global Lipschitz conditions. Then we also discuss L 2 -convergence under the local Lipschitz conditions.
ISSN:	1532-6349 1532-4214
DOI:	10.1080/15326349.2024.2398514