[COLLOQUIUM] Exponential ergodicity of McKean-Vlasov SDEs under Lyapunov conditions

Abstract: In this talk, we will discuss existence and uniqueness of solutions as well as existence of and exponential convergence to invariant measures for McKean-Vlasov stochastic differential equations with Markovian switching. Since the coefficients are only locally Lipschitz, we need to truncate them both in space and distribution variables simultaneously to get the global existence of solutions under the Lyapunov condition. Furthermore, if the Lyapunov condition is strengthened, we establish the exponential convergence of solutions' distributions to the unique invariant measure in Wasserstein quasi-distance and total variation distance, respectively. This is a joint work with Jun Ma.

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       柳振鑫教授简介：大连理工大学数学科学学院教授、院长。主要从事随机动力系统的研究，在随机Conley指标理论、随机动力系统中的回复性和稳定性、Kolmogorov平稳分布极限问题等方面做出系统深入的研究工作。目前已发表学术论文30余篇。2010年获全国百篇优秀博士学位论文提名奖；2015年获得国家优秀青年科学基金资助；2019年获得国家杰出青年科学基金资助。