论文标题
耦合的McKean-Vlasov随机微分方程与跳跃
Coupled McKean-Vlasov stochastic differential equations with jumps
论文作者
论文摘要
这项工作涉及一种耦合的McKean-Vlasov随机微分方程（简称MVSDE），并带有跳跃。首先，我们证明了这些耦合的MVSDE的叠加原理，并具有跳跃和非本地空间分布依赖于依赖的fokker-planck方程。由于叠加原理与跳跃耦合的MVSDE的弱解的适合性有关，因此我们给出一些条件以确保它。此后，我们构建了与这些耦合的MVSDE相关的空间分布的Markov过程。最后，研究了这些耦合的MVSD和跳跃的奇迹性。作为副产品，我们显示了具有跳跃的MVSDES类型的指数型成分。
This work concerns a type of coupled McKean-Vlasov stochastic differential equations (MVSDEs in short) with jumps. First, we prove superposition principles for these coupled MVSDEs with jumps and non-local space-distribution dependent Fokker-Planck equations. Since superposition principles are related to the well-posedness of weak solutions for coupled MVSDEs with jumps, then we give some conditions to assure it. After this, we construct space-distribution valued Markov processes associated with these coupled MVSDEs with jumps. Finally, the ergodicity of these coupled MVSDEs with jumps are investigated. As a by-product, we show the exponential ergodicity for a type of MVSDEs with jumps.
