Two-Level Bound for Stochastic Differential Equations Using the Exact Coupling with an Explicit Coefficients
We study a new method for the strong approximate solution of stochastic differential equations using coupling and we prove order one error bounds for Davie’s scheme (A. M. Davie, Pathwise approximation of stochastic differential equations using coupling, preprint: www.maths.ed.ac.uk/~adavie/coum.pdf ) in section (8) for the Lp
space assuming the invertibility of the diffusion matrix. In the prove we will use βikl
an explicit
versions for the diffusion instead of ρikl
which be used in Davie’s paper.
Keywords: Coupling; Euler Method for SDE; Milstein Method for Solving DSE; Numerical Solution of Stochastic Differential Equations; Stochastic Differential Equations (SDE)
Document Type: Research Article
Affiliations: Mathematics Department, College of Science, Qassim University, P. O. Box 6644, Buraydah 51452, Saudi Arabia; School of Mathematics, The Universty of Edinburgh, United Kingdom
Publication date: 01 June 2018
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