Wellposedness of conditional McKean-Vlasov equations with singular drifts and regime-switching

Abstract

<p style='text-indent:20px;'>This work is concerned with conditional McKean-Vlasov equations with regime-switching, which are indeed McKean-Vlasov SDEs with common noise. Due to the presence of the conditional distribution of the solution and regime-switching in the coefficients, the approach based on Zvonkin's transformation to deal with SDEs with singular coefficients no longer works directly and so need to be improved indispensably. In this work, we aim to provide a version of random Zvonkin's transformation to establish strong wellposedness for conditional McKean-Vlasov SDEs in a random environment.</p>