Strong convergence rate of the stochastic theta method for nonlinear hybrid stochastic differential equations with piecewise continuous arguments

Yuhang Zhang; Minghui Song; Mingzhu Liu; Bowen Zhao

doi:10.1007/s40314-022-02089-6

Strong convergence rate of the stochastic theta method for nonlinear hybrid stochastic differential equations with piecewise continuous arguments

Yuhang Zhang
, Minghui Song^*
, Mingzhu Liu
, Bowen Zhao

^*Corresponding author for this work

School of Mathematics, Harbin Institute of Technology

Research output: Contribution to journal › Article › peer-review

Abstract

We consider the strong convergence of the stochastic theta (ST) method for highly nonlinear hybrid stochastic differential equations with piecewise continuous arguments (SDEPCAs). There are three major ingredients. The first is the pth moment boundedness of the ST method. Second, the mean square convergence rate of the ST method for hybrid SDEPCAs is given by means of the forward–backward Euler–Maruyama method. The third ingredient is a numerical simulation, which shows the agreement with the theoretical convergence rate.

Original language	English
Article number	372
Journal	Computational and Applied Mathematics
Volume	41
Issue number	8
DOIs	https://doi.org/10.1007/s40314-022-02089-6
State	Published - Dec 2022
Externally published	Yes

Keywords

Convergence rate
Forward–backward Euler–Maruyama (FBEM) method
Stochastic differential equations with piecewise continuous arguments (SDEPCAs)
Stochastic theta (ST) method

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title = "Strong convergence rate of the stochastic theta method for nonlinear hybrid stochastic differential equations with piecewise continuous arguments",

abstract = "We consider the strong convergence of the stochastic theta (ST) method for highly nonlinear hybrid stochastic differential equations with piecewise continuous arguments (SDEPCAs). There are three major ingredients. The first is the pth moment boundedness of the ST method. Second, the mean square convergence rate of the ST method for hybrid SDEPCAs is given by means of the forward–backward Euler–Maruyama method. The third ingredient is a numerical simulation, which shows the agreement with the theoretical convergence rate.",

keywords = "Convergence rate, Forward–backward Euler–Maruyama (FBEM) method, Stochastic differential equations with piecewise continuous arguments (SDEPCAs), Stochastic theta (ST) method",

author = "Yuhang Zhang and Minghui Song and Mingzhu Liu and Bowen Zhao",

note = "Publisher Copyright: {\textcopyright} 2022, The Author(s) under exclusive licence to Sociedade Brasileira de Matem{\'a}tica Aplicada e Computacional.",

year = "2022",

month = dec,

doi = "10.1007/s40314-022-02089-6",

language = "英语",

volume = "41",

journal = "Computational and Applied Mathematics",

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TY - JOUR

T1 - Strong convergence rate of the stochastic theta method for nonlinear hybrid stochastic differential equations with piecewise continuous arguments

AU - Zhang, Yuhang

AU - Song, Minghui

AU - Liu, Mingzhu

AU - Zhao, Bowen

PY - 2022/12

Y1 - 2022/12

N2 - We consider the strong convergence of the stochastic theta (ST) method for highly nonlinear hybrid stochastic differential equations with piecewise continuous arguments (SDEPCAs). There are three major ingredients. The first is the pth moment boundedness of the ST method. Second, the mean square convergence rate of the ST method for hybrid SDEPCAs is given by means of the forward–backward Euler–Maruyama method. The third ingredient is a numerical simulation, which shows the agreement with the theoretical convergence rate.

AB - We consider the strong convergence of the stochastic theta (ST) method for highly nonlinear hybrid stochastic differential equations with piecewise continuous arguments (SDEPCAs). There are three major ingredients. The first is the pth moment boundedness of the ST method. Second, the mean square convergence rate of the ST method for hybrid SDEPCAs is given by means of the forward–backward Euler–Maruyama method. The third ingredient is a numerical simulation, which shows the agreement with the theoretical convergence rate.

KW - Convergence rate

KW - Forward–backward Euler–Maruyama (FBEM) method

KW - Stochastic differential equations with piecewise continuous arguments (SDEPCAs)

KW - Stochastic theta (ST) method

UR - https://www.scopus.com/pages/publications/85141095271

U2 - 10.1007/s40314-022-02089-6

DO - 10.1007/s40314-022-02089-6

M3 - 文章

AN - SCOPUS:85141095271

SN - 2238-3603

VL - 41

JO - Computational and Applied Mathematics

JF - Computational and Applied Mathematics

IS - 8

M1 - 372

ER -

Strong convergence rate of the stochastic theta method for nonlinear hybrid stochastic differential equations with piecewise continuous arguments

Abstract

Keywords

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