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 L\'evy 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 to the canonical L\'evy space.