Zero noise limit of a stochastic differential equation involving a local time

Kazumasa Kuwada, Taro Matsumura

Research output: Contribution to journalArticlepeer-review

Abstract

This paper studies the zero noise limit for the solution of a class of one-dimensional stochastic differential equations involving local time with irregular drift. These solutions are expected to approach one of the solutions to the ordinary differential equation formally obtained by cutting off the noise term. By determining the limit, we reveal that the presence of the local time really affects the asymptotic behavior, while it is observed only when intensity of the drift term is close to symmetric around the irregular point. Related with this problem, we also establish the Wentzel-Freidlin type large deviation principle.

Original languageEnglish
Pages (from-to)777-794
Number of pages18
JournalOsaka Journal of Mathematics
Volume55
Issue number4
Publication statusPublished - 2018 Oct 1

ASJC Scopus subject areas

  • Mathematics(all)

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