In this talk, we first introduce the background of Levy processes, and then present stochastic differential equations driven by Levy processes. In comparison to the standard Gaussian noise, Levy noise has more versatile and interesting with a wider range of applications. However, Levy noise makes the analysis more difficult owing to the discontinuity of its sample paths. We attempt to overcome this difficulty and discuss the existence and uniqueness of the solution as well as several stochastic stability criteria, etc.

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