A note on exponential almost sure stability of stochastic differential equation

Xuerong MAO; Qingshuo SONG; Dichuan YANG

doi:10.4134/BKMS.2014.51.1.221

A note on exponential almost sure stability of stochastic differential equation

Xuerong MAO, Qingshuo SONG, Dichuan YANG

Department of Mathematics

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

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Abstract

Our goal is to relax a sufficient condition for the exponential almost sure stability of a certain class of stochastic differential equations. Compared to the existing theory, we prove the almost sure stability, replacing Lipschitz continuity and linear growth conditions by the existence of a strong solution of the underlying stochastic differential equation. This result is extendable for the regime-switching system. An explicit example is provided for the illustration purpose. © 2014 The Korean Mathematical Society.

Original language	English
Pages (from-to)	221-227
Journal	Bulletin of the Korean Mathematical Society
Volume	51
Issue number	1
Online published	31 Jan 2014
DOIs	https://doi.org/10.4134/BKMS.2014.51.1.221
Publication status	Published - Jan 2014

Research Keywords

Almost sure stability
Besel squared process
Regime-switching
Stochastic differential equation

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title = "A note on exponential almost sure stability of stochastic differential equation",

abstract = "Our goal is to relax a sufficient condition for the exponential almost sure stability of a certain class of stochastic differential equations. Compared to the existing theory, we prove the almost sure stability, replacing Lipschitz continuity and linear growth conditions by the existence of a strong solution of the underlying stochastic differential equation. This result is extendable for the regime-switching system. An explicit example is provided for the illustration purpose. {\textcopyright} 2014 The Korean Mathematical Society.",

keywords = "Almost sure stability, Besel squared process, Regime-switching, Stochastic differential equation",

author = "Xuerong MAO and Qingshuo SONG and Dichuan YANG",

year = "2014",

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language = "English",

volume = "51",

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journal = "Bulletin of the Korean Mathematical Society",

issn = "1015-8634",

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T1 - A note on exponential almost sure stability of stochastic differential equation

AU - MAO, Xuerong

AU - SONG, Qingshuo

AU - YANG, Dichuan

PY - 2014/1

Y1 - 2014/1

N2 - Our goal is to relax a sufficient condition for the exponential almost sure stability of a certain class of stochastic differential equations. Compared to the existing theory, we prove the almost sure stability, replacing Lipschitz continuity and linear growth conditions by the existence of a strong solution of the underlying stochastic differential equation. This result is extendable for the regime-switching system. An explicit example is provided for the illustration purpose. © 2014 The Korean Mathematical Society.

AB - Our goal is to relax a sufficient condition for the exponential almost sure stability of a certain class of stochastic differential equations. Compared to the existing theory, we prove the almost sure stability, replacing Lipschitz continuity and linear growth conditions by the existence of a strong solution of the underlying stochastic differential equation. This result is extendable for the regime-switching system. An explicit example is provided for the illustration purpose. © 2014 The Korean Mathematical Society.

KW - Almost sure stability

KW - Besel squared process

KW - Regime-switching

KW - Stochastic differential equation

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U2 - 10.4134/BKMS.2014.51.1.221

DO - 10.4134/BKMS.2014.51.1.221

M3 - RGC 21 - Publication in refereed journal

SN - 1015-8634

VL - 51

SP - 221

EP - 227

JO - Bulletin of the Korean Mathematical Society

JF - Bulletin of the Korean Mathematical Society

IS - 1

ER -

A note on exponential almost sure stability of stochastic differential equation

Abstract

Research Keywords

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ECS: Markov Chain Approximation of Path Dependent Hybrid Control System

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A note on exponential almost sure stability of stochastic differential equation

Abstract

Research Keywords

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ECS: Markov Chain Approximation of Path Dependent Hybrid Control System

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