THE IT$\hat{O}$ INTEGRAL WITH RESPECT TO ANALOGUE OF WIENER PROCESS

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In this note, we define the It$\hat{o}$ integral with respect to analogue of Wiener process and investigate its various properties and examples.

R. Durrett, Probability : Theory and Examples, 2nd edition, Duxbury Press, 1996.
T. C. Gard, Introduction to Stochastic Differential Equations, MARCEL DEKKER, INC., 1988.
K. Ito, Differential equations determining Markov processes, Zenkoku Shijo Danwakai, 1942.
F. C. Klebaner, Introduction to Stochastic Calculus with Applications, Imperial College Press, 1998.
L. C. G. Rogers and D. Williams, Diffusions , Markov Processes and Martingales, Volume 2 : Ito Calculus, John Wiley & Sons, 1987.
K. S. Ryu and M. K. Im, A measure-valued analogue of Wiener measure and the measure-valued Feynman-Kac formula, Trans. Amer. Math. Soc. 354 (2002), 4921-4951. https://doi.org/10.1090/S0002-9947-02-03077-5