Taylor approximation of stochastic functional differential equations with the Poisson jump

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 [InlineEquation not available: see fulltext.]-norm when the drift and diffusion coefficients are Taylor approximations. © 2013 Wang et al.; licensee Springer.