Abstract
In the present paper, we are concerned with a class of stochastic functional differential delay equations with the Poisson jump, whose coefficients are general Taylor expansions of the coefficients of the initial equation. Taylor approximations are a useful tool to approximate analytically or numerically the coefficients of stochastic differential equations. The aim of this paper is to investigate the rate of approximation between the true solution and the numerical solution in the sense of the L p -norm when the drift and diffusion coefficients are Taylor approximations.
Highlights
Stochastic differential equations [ – ] have attracted a lot of attention, because the problems are academically challenging, and of a practical importance and have played an important role in many fields such as in option pricing, forecast of the growth of population, etc
Much work has been done on stochastic differential equations
One assumes that the system under consideration is governed by a principle of causality, that is, the future states of the system are independent of the past states and are determined solely by the present
Summary
Stochastic differential equations [ – ] have attracted a lot of attention, because the problems are academically challenging, and of a practical importance and have played an important role in many fields such as in option pricing, forecast of the growth of population, etc. (see, e.g., [ ]). Stochastic functional differential equations [ ] give a mathematical explanation for such a system. In general, it is impossible to find the explicit solution for stochastic functional differential equations with the Poisson jump.
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