Approximate solutions for a class of doubly perturbed stochastic differential equations

Wei Mao, Liangjian Hu, Xuerong Mao

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

In this paper, we study the Carathéodory approximate solution for a class of doubly perturbed stochastic differential equations (DPSDEs). Based on the Carathéodory approximation procedure, we prove that DPSDEs have a unique solution and show that the Carathéodory approximate solution converges to the solution of DPSDEs under the global Lipschitz condition. Moreover, we extend the above results to the case of DPSDEs with non-Lipschitz coefficients.

LanguageEnglish
Number of pages17
JournalAdvances in Difference Equations
Volume2018
Issue number1
DOIs
Publication statusPublished - 24 Jan 2018

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Stochastic Equations
Approximate Solution
Differential equations
Differential equation
Non-Lipschitz
Lipschitz condition
Unique Solution
Converge
Class
Coefficient
Approximation

Keywords

  • Carathéodory approximate solution
  • doubly perturbed stochastic differential equations
  • global Lipschitz condition
  • non-Lipschitz condition

Cite this

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Approximate solutions for a class of doubly perturbed stochastic differential equations. / Mao, Wei; Hu, Liangjian; Mao, Xuerong.

In: Advances in Difference Equations, Vol. 2018, No. 1, 24.01.2018.

Research output: Contribution to journalArticle

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AU - Hu, Liangjian

AU - Mao, Xuerong

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AB - In this paper, we study the Carathéodory approximate solution for a class of doubly perturbed stochastic differential equations (DPSDEs). Based on the Carathéodory approximation procedure, we prove that DPSDEs have a unique solution and show that the Carathéodory approximate solution converges to the solution of DPSDEs under the global Lipschitz condition. Moreover, we extend the above results to the case of DPSDEs with non-Lipschitz coefficients.

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KW - non-Lipschitz condition

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