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Zbl 1217.60046
Luo, Jiaowan; Zou, Jiezhong; Hou, Zhenting
Comparison principle and stability criteria for stochastic differential delay equations with Markovian switching. (English)
[J] Sci. China, Ser. A 46, No. 1, 129-138 (2003). ISSN 1006-9283; ISSN 1862-2763/e

Summary: We first obtain a comparison principle for nonlinear stochastic differential delay equations with Markovian switching. Later, using this comparison principle, we obtain some stability criteria, including stability in probability, asymptotic stability in probability, stability in the pth mean, asymptotic stability in the pth mean and the pth moment exponential stability of such equations. Finally, an example is given to illustrate the effectiveness of our results

MSC 2000:: *60H10 Stochastic ordinary differential equations
60H05 Stochastic integrals
34K50 Stochastic delay equations

Keywords: comparison principle; Brownian motion; stochastic differential delay equations; generalized Itô's formula; Markov chain

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