PARAMETER ESTIMATION OF PATH-DEPENDENT MCKEAN-VLASOV STOCHASTIC DIFFERENTIAL EQUATIONS

This work concerns a class of path-dependent Mc Kean-Vlasov stochastic differential equations with unknown parameters. First, we prove the existence and uniqueness of these equations under non-Lipschitz conditions. Second, we construct maximum likelihood estimators of these parameters and then discuss their strong consistency. Third, a numerical simulation method for the class of path-dependent Mc Kean-Vlasov stochastic differential equations is offered. Finally, we estimate the errors between solutions of these equations and that of their numerical equations.