Well-Posedness for McKean-Vlasov SDEs Driven by Multiplicative Stable Noises Changsong Deng Xi ng Huang Abstract We establish the well-posedness for a class of McKean-Vlasov SDEs driven by symmetric Q-stable Levy proc...Well-Posedness for McKean-Vlasov SDEs Driven by Multiplicative Stable Noises Changsong Deng Xi ng Huang Abstract We establish the well-posedness for a class of McKean-Vlasov SDEs driven by symmetric Q-stable Levy processes(1/2<α≤1),where the drift coefficient is Holder continuous in space variable,while the noise coeficient is Lipscitz continuous in space variable,and both of them satisfy the Lipschitz condition in distribution variable with respect to Wasserstein distance.If the drift coefficient does not depend on distribution variable,our methodology developed in this paper applies to the caseαe(0,1].The main tool relies on heat kernel estimates for(distribution independent)stable SDEs and Banach's fixed point theorem.展开更多
We study the functional limits of continuous-time random walks （CTRWs） with tails under certain conditions. We find that the scaled CTRWs with tails converge weakly to an a-stable Levy process in D（[0, 1]） with M1...We study the functional limits of continuous-time random walks （CTRWs） with tails under certain conditions. We find that the scaled CTRWs with tails converge weakly to an a-stable Levy process in D（[0, 1]） with M1-topology but the corresponding scaled CTRWs converge weakly to the same limit in D（[0, 1]） with J1-topology.展开更多
文摘Well-Posedness for McKean-Vlasov SDEs Driven by Multiplicative Stable Noises Changsong Deng Xi ng Huang Abstract We establish the well-posedness for a class of McKean-Vlasov SDEs driven by symmetric Q-stable Levy processes(1/2<α≤1),where the drift coefficient is Holder continuous in space variable,while the noise coeficient is Lipscitz continuous in space variable,and both of them satisfy the Lipschitz condition in distribution variable with respect to Wasserstein distance.If the drift coefficient does not depend on distribution variable,our methodology developed in this paper applies to the caseαe(0,1].The main tool relies on heat kernel estimates for(distribution independent)stable SDEs and Banach's fixed point theorem.
基金Acknowledgements The author thanks Professor Yimin Xiao for stimulating discussion. Thanks are also due to the anonymous referees for their careful reading and useful suggestions. This work was supported in part by the National Natural Science Foundation of China （Grant No. 10901054）.
文摘We study the functional limits of continuous-time random walks （CTRWs） with tails under certain conditions. We find that the scaled CTRWs with tails converge weakly to an a-stable Levy process in D（[0, 1]） with M1-topology but the corresponding scaled CTRWs converge weakly to the same limit in D（[0, 1]） with J1-topology.
