论文标题
Markovian Switching的Lyapunov条件下的Lyapunov条件下的存在，独特性和指数性千古
Existence, uniqueness and exponential ergodicity under Lyapunov conditions for McKean-Vlasov SDEs with Markovian switching
论文作者
论文摘要
该论文致力于研究解决方案的存在和独特性以及与马尔可夫开关的McKean-Vlasov随机微分方程的不变措施的存在和指数融合。由于系数仅是局部Lipschitz，因此我们需要同时在空间和分布变量中截断它们，以使在Lyapunov条件下的全局溶液存在。此外，如果加强了Lyapunov条件，我们将分别在Wasserstein Quasi-Distance和总变化距离中建立了解决方案分布与独特不变度的指数收敛。最后，我们提供了两个应用程序来说明我们的理论结果。
The paper is dedicated to studying the problem of 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. Finally, we give two applications to illustrate our theoretical results.
