Existence and Uniqueness Solution for a Semimartingale Stochastic Integral Equation - Abd Alhafid, Hanan Salem (Scientific Journal of University of Benghazi, 2023)
This paper studied existence and uniqueness of a solution for a semimartingale stochastic integral equation by using Existence and Uniqueness Theorem on the martingale process. Using the concept of convergence Cauchy sequence to a cadlag process , where , we can find a convergence Cauchy sequence to a cadlag process on the space of martingales, where is a square-integrable cadlag martingale on a probability space , as = . And some important assumptions are is a map from the space into the space of -matrices. satisfies a spatial Lipschitz condition uniformly in the other variables: for each there exists a finite constant such that this holds for and all : . ii. Given any adapted -valued cadlag process on , the function is a predictable process, and there exist stopping times such that is bounded for each .