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arXiv · 1602.08160

Stability of stochastic differential equations with respect to time-changed Brownian motions

Qiong Wu
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Abstract

In this paper, the stability behaviors of stochastic differential equations (SDEs) driven by time-changed Brownian motions are discussed. Based on the generalized Lyapunov method and stochastic analysis, necessary conditions are provided for solutions of time-changed SDEs to be stable in differential senses, such as stochastic stability, stochastically asymptotic stability and globally stochastically asymptotic stability. Also, a connection between the stability of the solution to the time-changed SDEs and that to their corresponding non-time-changed SDEs is revealed by applying the duality theorem. Finally, two examples are provided to illustrate the theoretical results.

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Qiong Wu. 2016-02-26. Stability of stochastic differential equations with respect to time-changed Brownian motions. https://arxiv.org/abs/1602.08160

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