Razumikhin-type theorems on exponential stability of SDDEs containing singularly perturbed random processes

Junhao Hu, Xuerong Mao, Chenggui Yuan

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

This paper concerns Razumikhin-type theorems on exponential stability of stochastic differential delay equations with Markovian switching, where the modulating Markov chain involves small parameters. The smaller the parameter is, the rapider switching the system will experience. In order to reduce the complexity, we will “replace” the original systems by limit systems with a simple structure. Under Razumikhin-type conditions, we establish theorems that if the limit systems are pth-moment exponentially stable; then, the original systems are pth-moment exponentially stable in an appropriate sense.

LanguageEnglish
Article number854743
Number of pages13
JournalAbstract and Applied Analysis
Volume2013
DOIs
Publication statusPublished - 2013

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Random process
Exponential Stability
Singularly Perturbed
Asymptotic stability
Random processes
Theorem
Markov processes
Stochastic Differential Delay Equations
Moment
Markovian Switching
Small Parameter
Markov chain

Keywords

  • Razumikhin-type theorem
  • Markovian switching
  • stochastic differential delay equations
  • exponential stability
  • Markov Chain
  • small parameters

Cite this

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title = "Razumikhin-type theorems on exponential stability of SDDEs containing singularly perturbed random processes",
abstract = "This paper concerns Razumikhin-type theorems on exponential stability of stochastic differential delay equations with Markovian switching, where the modulating Markov chain involves small parameters. The smaller the parameter is, the rapider switching the system will experience. In order to reduce the complexity, we will “replace” the original systems by limit systems with a simple structure. Under Razumikhin-type conditions, we establish theorems that if the limit systems are pth-moment exponentially stable; then, the original systems are pth-moment exponentially stable in an appropriate sense.",
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author = "Junhao Hu and Xuerong Mao and Chenggui Yuan",
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language = "English",
volume = "2013",
journal = "Abstract and Applied Analysis",
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Razumikhin-type theorems on exponential stability of SDDEs containing singularly perturbed random processes. / Hu, Junhao; Mao, Xuerong; Yuan, Chenggui.

In: Abstract and Applied Analysis, Vol. 2013, 854743, 2013.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Razumikhin-type theorems on exponential stability of SDDEs containing singularly perturbed random processes

AU - Hu, Junhao

AU - Mao, Xuerong

AU - Yuan, Chenggui

PY - 2013

Y1 - 2013

N2 - This paper concerns Razumikhin-type theorems on exponential stability of stochastic differential delay equations with Markovian switching, where the modulating Markov chain involves small parameters. The smaller the parameter is, the rapider switching the system will experience. In order to reduce the complexity, we will “replace” the original systems by limit systems with a simple structure. Under Razumikhin-type conditions, we establish theorems that if the limit systems are pth-moment exponentially stable; then, the original systems are pth-moment exponentially stable in an appropriate sense.

AB - This paper concerns Razumikhin-type theorems on exponential stability of stochastic differential delay equations with Markovian switching, where the modulating Markov chain involves small parameters. The smaller the parameter is, the rapider switching the system will experience. In order to reduce the complexity, we will “replace” the original systems by limit systems with a simple structure. Under Razumikhin-type conditions, we establish theorems that if the limit systems are pth-moment exponentially stable; then, the original systems are pth-moment exponentially stable in an appropriate sense.

KW - Razumikhin-type theorem

KW - Markovian switching

KW - stochastic differential delay equations

KW - exponential stability

KW - Markov Chain

KW - small parameters

U2 - 10.1155/2013/854743

DO - 10.1155/2013/854743

M3 - Article

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JO - Abstract and Applied Analysis

T2 - Abstract and Applied Analysis

JF - Abstract and Applied Analysis

SN - 1085-3375

M1 - 854743

ER -