Nonlocal stochastic differential equations: Existence and uniqueness of solutions

Abstract

The focus of interest is the existence of strong solutions to stochastic functional differential equations which are not restricted to pathwise dependencies. Indeed, the evolution of the wanted random process may be prescribed by its current features being nonlocal with respect to the probability space — like the expected value and second moments. This result is concluded from Cauchy-Lipschitz Theorem for mutational equations (a form of generalized ODEs beyond vector spaces) and a new aspect of weakening their a priori requirements.