分野別セミナー

Averaging principle is a kind of theorem that can simplify the original system with its solution converging to the so-called averaged system in the sense of probability. The stochastic averaging method is developed to obtain the response solutions including the probability density function and sample path solutions where the reduced system is usually established via the stochastic averaging technique. Then the noise-induced dynamics for different conceptual dynamical system will be presented. In this talk, we will talk about the Non-Gaussian Levy noise which describes the model of random fluctuations beyond the Gaussian noise. The averaging principle in the presence of Levy noise will be proposed mathematically for SDEs/SPDEs under (non) Lipschitz conditions, and here these main results will support the method of stochastic averaging theoretically. Based on the developed techniques we will further talk the levy noise-induced dynamics including the stochastic bifurcation and transitions. The different effects of levy noise from Gaussian case will be demonstrated especially for the alpha stable Levy noise. This is a joint work with Yongge Li, Bin Pei, Qi Liu, Wei Xu and Juergen Kurths.