Asymptotic behaviours of stochastic differential delay equations

Shen, Yi and Mao, Xuerong (2006) Asymptotic behaviours of stochastic differential delay equations. Asian Journal of Control, 8 (1). 21–27. ISSN 1561-8625 (https://doi.org/10.1111/j.1934-6093.2006.tb00247.x)

PDF. Filename: P2_2_.pdf Accepted Author Manuscript Download (194kB)

Abstract

Most of the existing results on stochastic stability use a single Lyapunov function, but we shall instead use multiple Lyapunov functions in this paper. We shall establish the sufficient condition, in terms of multiple Lyapunov functions, for the asymptotic behaviours of solutions of stochastic differential delay equations. Moreover, from them follow many effective criteria on stochastic asymptotic stability, which enable us to construct the Lyapunov functions much more easily in applications. In particular, the well-known classical theorem on stochastic asymptotic stability is a special case of our more general results. These show clearly the power of our new results. Two examples are also given for illustration.

• Share and Export
  

  RDF+XMLBibTeXRIOXX2 XMLRDF+N-TriplesJSONDublin CoreAtomSimple MetadataReferMETSHTML CitationASCII CitationOpenURL ContextObjectEndNoteOpenURL ContextObject in SpanMODSMPEG-21 DIDLEP3 XMLData Cite XMLRIS (EndNote Online, Zotero, Ref manager, etc)RDF+N3Multiline CSV
• Item metadata

  Item type:	Article
  ID code:	47417
  Dates:	Date Event March 2006 Published
  Notes:	This paper relates to 2006 EPSRC project entitled Asymptotic stability of neutral-type stochastic functional differential equations; Collaborative research visit to China
  Subjects:	Science > Mathematics > Probabilities. Mathematical statistics
  Department:	Faculty of Science > Mathematics and Statistics
  Depositing user:	Pure Administrator
  Date deposited:	09 Apr 2014 12:45
  Last modified:	22 Apr 2024 00:24
  URI:	https://strathprints.strath.ac.uk/id/eprint/47417