Wu, Fuke and Mao, Xuerong and Szpruch, Lukasz (2010) Almost sure exponential stability of numerical solutions for stochastic delay differential equations. Numerische Mathematik, 115 (4). pp. 681-697.
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Using techniques based on the continuous and discrete semimartingale convergence theorems, this paper investigates if numerical methods may reproduce the almost sure exponential stability of the exact solutions to stochastic delay differential equations (SDDEs). The important feature of this technique is that it enables us to study the almost sure exponential stability of numerical solutions of SDDEs directly. This is significantly different from most traditional methods by which the almost sure exponential stability is derived from the moment stability by the Chebyshev inequality and the Borel–Cantelli lemma.
|Keywords:||numerical solutions , stochastic delay , differential equations , Probabilities. Mathematical statistics, Computational Mathematics, Applied Mathematics|
|Subjects:||Science > Mathematics > Probabilities. Mathematical statistics|
|Department:||Faculty of Science > Mathematics and Statistics|
|Depositing user:||Pure Administrator|
|Date Deposited:||07 Mar 2011 23:25|
|Last modified:||28 Apr 2016 07:45|