Linear stochastic differential equations with anticipating initial conditions

In this paper we use the new stochastic integral introduced by Ayed and Kuo [1] and the results obtained by Kuo, Sae-Tang and Szozda [10] to find a solution to a drift-free linear stochastic differential equation with anticipating initial condition. Our solution is based on well-known results from classical Itô theory and anticipative Itô formula results from [10]. We also show that the solution obtained by our method is consistent with the solution obtained by the methods of Malliavin calculus, see e.g., [3].