Almost sure exponential stability of the theta-method for stochastic differential equations

Lin Chen, Fuke Wu

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13 Citations (Scopus)

Abstract

Our previous work shows that the backward Euler-Maruyama (BEM) method may reproduce the almost sure stability of stochastic differential equations (SDEs) without the linear growth condition for the drift coefficient (see Wu et al. (2010)) but the Euler-Maruyama (EM) method cannot. It is well known that the theta-method is more general and may be specialized as the BEM and EM by choosing theta = 1 and theta = 0. Then it is very interesting to examine the interval in which the theta-method holds the same stability property as the BEM method. This paper shows that when theta is an element of (1/2, 1], the theta-method may reproduce the almost sure stability of the exact solution of SDEs. Finally, a two-dimensional example is presented to illustrate this result.
Original languageEnglish
Pages (from-to)1669 - 1676
Number of pages8
JournalStatistics and Probability Letters
Volume82
Issue number9
DOIs
Publication statusPublished - 2012
Externally publishedYes

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