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Practical Stability in the th Mean for Itô Stochastic Differential Equations

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  • Enguang Miao
  • Huisheng Shu
  • Yan Che

Abstract

The th mean practical stability problem is studied for a general class of Itô-type stochastic differential equations over both finite and infinite time horizons. Instead of the comparison principle, a function which is nonnegative, nondecreasing, and differentiable is cooperated with the Lyapunov-like functions to analyze the practical stability. By using this technique, the difficulty in finding an auxiliary deterministic stable system is avoided. Then, some sufficient conditions are established that guarantee the th moment practical stability of the considered equations. Moreover, the practical stability is compared with traditional Lyapunov stability; some differences between them are given. Finally, the results derived in this paper are demonstrated by an illustrative example.

Suggested Citation

  • Enguang Miao & Huisheng Shu & Yan Che, 2012. "Practical Stability in the th Mean for Itô Stochastic Differential Equations," Mathematical Problems in Engineering, Hindawi, vol. 2012, pages 1-12, October.
    • Handle: RePEc:hin:jnlmpe:380304
    DOI: 10.1155/2012/380304
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