Approximate solutions for a class of doubly perturbed stochastic differential equations

Wei Mao; Liangjian Hu; Xuerong Mao

doi:10.1186/s13662-018-1490-5

Approximate solutions for a class of doubly perturbed stochastic differential equations

Wei Mao^*, Liangjian Hu, Xuerong Mao

^*Corresponding author for this work

Mathematics And Statistics

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

14 Citations (Scopus)

42 Downloads (Pure)

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.

Original language	English
Number of pages	17
Journal	Advances in Difference Equations
Volume	2018
Issue number	1
DOIs	https://doi.org/10.1186/s13662-018-1490-5
Publication status	Published - 24 Jan 2018

Keywords

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

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10.1186/s13662-018-1490-5Licence: CC BY 4.0

Mao-etal-ADE-2018-Approximate-solutions-for-a-class-of-doubly-perturbed-stochastic-differential-equationsFinal published version, 1.32 MBLicence: CC BY 4.0

Cite this

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title = "Approximate solutions for a class of doubly perturbed stochastic differential equations",

abstract = "In this paper, we study the Carath{\'e}odory approximate solution for a class of doubly perturbed stochastic differential equations (DPSDEs). Based on the Carath{\'e}odory approximation procedure, we prove that DPSDEs have a unique solution and show that the Carath{\'e}odory 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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AU - Mao, Wei

AU - Hu, Liangjian

AU - Mao, Xuerong

PY - 2018/1/24

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N2 - 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.

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.

KW - Carathéodory approximate solution

KW - doubly perturbed stochastic differential equations

KW - global Lipschitz condition

KW - non-Lipschitz condition

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VL - 2018

JO - Advances in Difference Equations

JF - Advances in Difference Equations

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Approximate solutions for a class of doubly perturbed stochastic differential equations

Abstract

Keywords

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Long-time dynamics of numerical solutions of stochastic differential equations

Numerical Analysis of Stochastic Differential Equations: New Challenges

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Approximate solutions for a class of doubly perturbed stochastic differential equations

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Projects

Long-time dynamics of numerical solutions of stochastic differential equations

Numerical Analysis of Stochastic Differential Equations: New Challenges

Cite this