Distribution dependent SDEs for Landau type equations

作者：Wang, Feng-Yu^*

来源：Stochastic Processes and Their Applications, 2018, 128(2): 595-621.

DOI：10.1016/j.spa.2017.05.006

• Distribution dependent SDEs
• Homogeneous Landau equation
• Wasserstein distance
• Exponential convergence
• Harnack inequality

The distribution dependent stochastic differential equations (DDSDEs) describe stochastic systems whose evolution is determined by both the microcosmic site and the macrocosmic distribution of the particle. The density function associated with a DDSDE solves a nonlinear PDE. Due to the distribution dependence, some standard techniques developed for SDEs do not apply. By iterating in distributions, a strong solution is constructed using SDEs with control. By proving the uniqueness, the distribution of solutions is identified with a nonlinear semigroup P-t* on the space of probability measures. The exponential contraction as well as Harnack inequalities and applications are investigated for the nonlinear semigroup Pt* using coupling by change of measures. The main results are illustrated by homogeneous Landau equations.

• 出版日期2018-2
• 单位天津大学