Linear stochastic differential equations with anticipating initial conditions

Narjess Khalifa, Hui-Hsiung Kuo
2013 Communications on Stochastic Analysis  
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
more » ... f Malliavin calculus, see e.g., [3] . Received 2012-12-20; Communicated by the editors. 2000 Mathematics Subject Classification. Primary 60H05; Secondary 60H20.
doi:10.31390/cosa.7.2.05 fatcat:zc77o6nhqfbjxo4eygxnixakum