Anticipating linear stochastic differential equations driven by a Lévy process

Abstract

In this paper we study the existence of a unique solution for linear stochastic differential equations driven by a Lévy process, where the initial condition and the coefficients are random and not necessarily adapted to the underlying filtration. Towards this end, we extend the method based on Girsanov transformation on Wiener space and developped by Buckdahn [7] to the canonical Lévy space, which is introduced in [25].