Abstract
In this paper, existence, uniqueness and continuity of the a dapted solutions for neutral stochastic delay Volterra equations with singular kernels are discussed. In addition , continuous dependence on the initial date is also investigated. Finally, stochastic Volterra equation with the kernel of fractional Brownian motion is studied to illustrate the effectiveness of our results.
Highlights
This paper is concerned with solutions of neutral stochastic delay Volterra equations (NSDVE) driven by Poisson random measure as follows: t t
X(t) =x + f (t, s, X(s))ds + g(t, s, X(s))dB(s). Such equations arise in many applications such as mathematical finance, biology. etc
Some results of backward stochastic volterra equations were obtained, which can be used for discussing mathematical finance and stochastic optimal control
Summary
This paper is concerned with solutions of neutral stochastic delay Volterra equations (NSDVE) driven by Poisson random measure as follows:. Stochastic Volterra equation(SVE) was first studied by Berger and Mizel ( [1], [2]) for equations: X(t) =x + f (t, s, X(s))ds + g(t, s, X(s))dB(s). Wang [11] proved that there exists a unique continuous adapted solution to SVE with singular kernels. Studied the numerical solutions and the large deviation principles of Freidlin-Wentzell’s type for SVE with singular kernels. We prove the existence, uniqueness and continuity of the adapted solutions to NSDVE with singular kernels.
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