Open AccessThe truncated Milstein method for super-linear stochastic differential equations with Markovian switching
Author(s) -
Weijun Zhan,
Qian Guo,
Yuhao Cong
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series b
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.864
H-Index - 53
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2021201
Subject(s) - mathematics , markov chain , convergence (economics) , stochastic differential equation , rate of convergence , markov process , order (exchange) , computer science , statistics , key (lock) , economics , economic growth , finance , computer security
In this paper, to approximate the super-linear stochastic differential equations modulated by a Markov chain, we investigate a truncated Milstein method with convergence order 1 in the mean-square sense. Under Khasminskii-type conditions, we establish the convergence result by employing a relationship between local and global errors. Finally, we confirm the convergence rate by a numerical example.