TY - JOUR
T1 - Singular McKean–Vlasov SDEs
T2 - Well-posedness, regularities and Wang's Harnack inequality
AU - Ren, Panpan
PY - 2023/2
Y1 - 2023/2
N2 - The well-posedness and regularity estimates in initial distributions are derived for singular McKean–Vlasov SDEs, where the drift contains a locally standard integrable term and a superlinear term in the spatial variable, and is Lipschitz continuous in the distribution variable with respect to a weighted variation distance. When the superlinear term is strengthened to be Lipschitz continuous, Wang's Harnack inequality is established. These results are new also for the classical Itô SDEs where the coefficients are distribution independent.
AB - The well-posedness and regularity estimates in initial distributions are derived for singular McKean–Vlasov SDEs, where the drift contains a locally standard integrable term and a superlinear term in the spatial variable, and is Lipschitz continuous in the distribution variable with respect to a weighted variation distance. When the superlinear term is strengthened to be Lipschitz continuous, Wang's Harnack inequality is established. These results are new also for the classical Itô SDEs where the coefficients are distribution independent.
KW - Regularities
KW - Singular McKean–Vlasov SDE
KW - Wang's Harnack inequality
UR - http://www.scopus.com/inward/record.url?scp=85144070037&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85144070037&origin=recordpage
U2 - 10.1016/j.spa.2022.11.010
DO - 10.1016/j.spa.2022.11.010
M3 - RGC 21 - Publication in refereed journal
SN - 0304-4149
VL - 156
SP - 291
EP - 311
JO - Stochastic Processes and their Applications
JF - Stochastic Processes and their Applications
ER -