Convergence and stability of impulsive stochastic differential equations

M. H. Song; H. Z. Yang; M. Z. Liu

doi:10.1080/00207160.2016.1227798

Convergence and stability of impulsive stochastic differential equations

M. H. Song^*
, H. Z. Yang
, M. Z. Liu

^*Corresponding author for this work

School of Mathematics

Harbin Institute of Technology

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

6 Scopus citations

Abstract

In this paper, we consider impulsive stochastic differential equations. We show that these equations are the exponentially stable in the mean-square sense under Lipschitz conditions. We also construct the numerical method and prove the method is strongly convergent and exponentially stable in the mean-square sense. Moreover, we give some examples in order to illustrate the main results.

Original language	English
Pages (from-to)	1738-1746
Number of pages	9
Journal	International Journal of Computer Mathematics
Volume	94
Issue number	9
DOIs	https://doi.org/10.1080/00207160.2016.1227798
State	Published - 2 Sep 2017

Keywords

Impulsive stochastic differential equations
convergence
exponential stability
simulation
transformed-Euler method

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10.1080/00207160.2016.1227798

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title = "Convergence and stability of impulsive stochastic differential equations",

abstract = "In this paper, we consider impulsive stochastic differential equations. We show that these equations are the exponentially stable in the mean-square sense under Lipschitz conditions. We also construct the numerical method and prove the method is strongly convergent and exponentially stable in the mean-square sense. Moreover, we give some examples in order to illustrate the main results.",

keywords = "Impulsive stochastic differential equations, convergence, exponential stability, simulation, transformed-Euler method",

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T1 - Convergence and stability of impulsive stochastic differential equations

AU - Song, M. H.

AU - Yang, H. Z.

AU - Liu, M. Z.

PY - 2017/9/2

Y1 - 2017/9/2

N2 - In this paper, we consider impulsive stochastic differential equations. We show that these equations are the exponentially stable in the mean-square sense under Lipschitz conditions. We also construct the numerical method and prove the method is strongly convergent and exponentially stable in the mean-square sense. Moreover, we give some examples in order to illustrate the main results.

AB - In this paper, we consider impulsive stochastic differential equations. We show that these equations are the exponentially stable in the mean-square sense under Lipschitz conditions. We also construct the numerical method and prove the method is strongly convergent and exponentially stable in the mean-square sense. Moreover, we give some examples in order to illustrate the main results.

KW - Impulsive stochastic differential equations

KW - convergence

KW - exponential stability

KW - simulation

KW - transformed-Euler method

UR - https://www.scopus.com/pages/publications/84988731320

U2 - 10.1080/00207160.2016.1227798

DO - 10.1080/00207160.2016.1227798

M3 - 文章

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VL - 94

SP - 1738

EP - 1746

JO - International Journal of Computer Mathematics

JF - International Journal of Computer Mathematics

IS - 9

ER -

Convergence and stability of impulsive stochastic differential equations

Abstract

Keywords

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