Stochastic versions of the LaSalle theorem

X. Mao

doi:10.1006/jdeq.1998.3552

Stochastic versions of the LaSalle theorem

X. Mao^*

^*Corresponding author for this work

Mathematics And Statistics

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

209 Citations (Scopus)

Abstract

The main aim of this paper is to establish stochastic versions of the well-known LaSalle stability theorem. From these stochastic versions follow many classical results on stochastic stability. This shows clearly the power of our new results.

Original language	English
Pages (from-to)	175-195
Number of pages	21
Journal	Journal of Differential Equations
Volume	153
Issue number	1
DOIs	https://doi.org/10.1006/jdeq.1998.3552
Publication status	Published - 20 Mar 1999

Keywords

Itô's formula
LaSalle's theorem
Lyapunov function
supermartingale convergence theorem

Access to Document

10.1006/jdeq.1998.3552Licence: Other

Cite this

@article{84084a3dae9843c289faa78705fa925d,

title = "Stochastic versions of the LaSalle theorem",

abstract = "The main aim of this paper is to establish stochastic versions of the well-known LaSalle stability theorem. From these stochastic versions follow many classical results on stochastic stability. This shows clearly the power of our new results.",

keywords = "It{\^o}'s formula, LaSalle's theorem, Lyapunov function, supermartingale convergence theorem",

author = "X. Mao",

year = "1999",

month = mar,

day = "20",

doi = "10.1006/jdeq.1998.3552",

language = "English",

volume = "153",

pages = "175--195",

journal = "Journal of Differential Equations",

issn = "0022-0396",

publisher = "Academic Press Inc.",

number = "1",

}

TY - JOUR

T1 - Stochastic versions of the LaSalle theorem

AU - Mao, X.

PY - 1999/3/20

Y1 - 1999/3/20

N2 - The main aim of this paper is to establish stochastic versions of the well-known LaSalle stability theorem. From these stochastic versions follow many classical results on stochastic stability. This shows clearly the power of our new results.

AB - The main aim of this paper is to establish stochastic versions of the well-known LaSalle stability theorem. From these stochastic versions follow many classical results on stochastic stability. This shows clearly the power of our new results.

KW - Itô's formula

KW - LaSalle's theorem

KW - Lyapunov function

KW - supermartingale convergence theorem

UR - http://www.scopus.com/inward/record.url?scp=0033586169&partnerID=8YFLogxK

U2 - 10.1006/jdeq.1998.3552

DO - 10.1006/jdeq.1998.3552

M3 - Article

AN - SCOPUS:0033586169

SN - 0022-0396

VL - 153

SP - 175

EP - 195

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 1

ER -

Stochastic versions of the LaSalle theorem

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this