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Almost sure exponential stability of backward Euler–Maruyama discretizations for hybrid stochastic differential equations

✍ Scribed by Xuerong Mao; Yi Shen; Alison Gray

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
392 KB
Volume
235
Category
Article
ISSN
0377-0427

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✦ Synopsis

This is a continuation of the first author's earlier paper [1] jointly with Pang and Deng, in which the authors established some sufficient conditions under which the Euler-Maruyama (EM) method can reproduce the almost sure exponential stability of the test hybrid SDEs. The key condition imposed in [1] is the global Lipschitz condition. However, we will show in this paper that without this global Lipschitz condition the EM method may not preserve the almost sure exponential stability. We will then show that the backward EM method can capture the almost sure exponential stability for a certain class of highly nonlinear hybrid SDEs.

📜 SIMILAR VOLUMES

Almost sure and moment exponential stabi
Almost sure and moment exponential stability of Euler–Maruyama discretizations for hybrid stochastic differential equations
✍ Sulin Pang; Feiqi Deng; Xuerong Mao 📂 Article 📅 2008 🏛 Elsevier Science 🌐 English ⚖ 214 KB

Positive results are derived concerning the long time dynamics of numerical simulations of stochastic differential equation systems with Markovian switching. Euler-Maruyama discretizations are shown to capture almost sure and moment exponential stability for all sufficiently small timesteps under ap