Difference methods for stochastic differential equations with discontinuous coefficients
- 1 September 1984
- journal article
- research article
- Published by Taylor & Francis in Stochastics
- Vol. 13 (3) , 199-212
- https://doi.org/10.1080/17442508408833318
Abstract
In this paper it is proved that the solution of the stochastic (vector)-differential equation dx(t) = a(t,x(t))dt + b(t,x(t)) dw(t) can be approximated in a weak sense (convergence of distributions) by the Euler method x$sub:n + l$esub:=x$sub:n$esub: + a(t$sub:n$esub:,x$sub:n$esub:)ßt + b(t$sub:n$esub:,x$sub:n$esub:)w$sub:n$esub:, where the w$sub:n$esub:are independent, normally distributed random variables with mean zero and variance ßt, if the coefficients are Lipschitz-continuous outside of a finite set of switching curves and b is a uniformly positive definite matrix.Keywords
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