Asymptotic behavior of solutions of linear stochastic differential systems

Avner Friedman, Mark A. Pinsky

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

Abstract

Following Kasminski, we investigate asymptotic behavior of solutions of linear time-independent Ito equations. We first give a sufficient condition for asymptotic stability of the zero solution. Then in dimension 2 we determine conditions for spiraling at a linear rate. Finally we give applications to the Cauchy problem for the associated parabolic equation by the use of a tauberian theorem.

Original languageEnglish (US)
Pages (from-to)1-22
Number of pages22
JournalTransactions of the American Mathematical Society
Volume181
DOIs
StatePublished - Jul 1973

Keywords

  • Asymptotic stability
  • Diffusion process
  • Spiraling solutions
  • Stochastic differential equation

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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