 Almost sure exponential stability of the θ-method for stochastic differential equationsLin Chen and Fuke Wu Statistics & Probability Letters, 2012, vol. 82, issue 9, 1669-1676 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 θ-method is more general and may be specialized as the BEM and EM by choosing θ=1 and θ=0. Then it is very interesting to examine the interval in which the θ-method holds the same stability property as the BEM method. This paper shows that when θ∈(1/2,1], the θ-method may reproduce the almost sure stability of the exact solution of SDEs. Finally, a two-dimensional example is presented to illustrate this result. Keywords: Stochastic differential equations; Almost sure exponential stability; θ-method; Semimartingale convergence theorem; One-sided linear growth (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:stapro:v:82:y:2012:i:9:p:1669-1676 Ordering information: This journal article can be ordered from DOI: 10.1016/j.spl.2012.05.004 Access Statistics for this article Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul More articles in Statistics & Probability Letters from Elsevier |
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