Doctor of Philosophy (PhD)
In this work, we develop further the theory of stochastic integration of adapted and instantly independent stochastic processes started by Wided Ayed and Hui-Hsiung Kuo in [1,2]. We provide a first counterpart to the Itô isometry that accounts for both adapted and instantly independent processes. We also present several Itô formulas for the new stochastic integral. Finally, we apply the new Itô formula to solve a linear stochastic differential equations with anticipating initial conditions.
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Szozda, Benedykt, "The new stochastic integral and anticipating stochastic differential equations" (2012). LSU Doctoral Dissertations. 1067.