The truncated Milstein method for super-linear stochastic differential equations with Markovian switching | Zendy

Weijun Zhan | Zendy; Qian Guo | Zendy; Yuhao Cong | Zendy

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The truncated Milstein method for super-linear stochastic differential equations with Markovian switching

Author(s) -

Weijun Zhan,

Qian Guo,

Yuhao Cong

Publication year - 2021

Publication title -

discrete and continuous dynamical systems - 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.

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