Existence and Uniqueness Solution for a Semimartingale Stochastic Integral Equation
DOI:
https://doi.org/10.37376/sjuob.v36i1.3934Keywords:
A Semimartingale Process, Stochastic Integral Equation, Lipschitz Condition, Stopped ProcessAbstract
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 .
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