Finite Difference Schemes for Linear Stochastic Integro-Differential
  Equations

doi:10.1016/j.spa.2016.04.025

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Finite Difference Schemes for Linear Stochastic Integro-Differential Equations

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Author(s): Konstantinos Dareiotis , James-Michael Leahy

Publication date Created: 2013-10-15

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Abstract

We study the rate of convergence of an explicit and an implicit-explicit finite difference scheme for linear stochastic integro-differential equations of parabolic type arising in non-linear filtering of jump-diffusion processes. We show that the rate is of order one in space and order one-half in time.

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Rate of Convergence of Space Time Approximations for stochastic evolution equations

Annie Millet, Istvan Gyongy (2007)

Stochastic evolution equations in Banach spaces with unbounded nonlinear drift and diffusion operators driven by a finite dimensional Brownian motion are considered. Under some regularity condition assumed for the solution, the rate of convergence of various numerical approximations are estimated under strong monotonicity and Lipschitz conditions. The abstract setting involves general consistency conditions and is then applied to a class of quasilinear stochastic PDEs of parabolic type.