The Law of the Euler Scheme for Stochastic Differential Equations: I. Convergence Rate of the Distribution Function

Abstract

We study the approximation problem of IEf(XT ) by IEf(Xn T ), where (Xt) is the solution of a stochastic differential equation, (Xn t ) is defined by the Euler discretization scheme with step Tn , and f is a given function. For smooth f ’s, Talay and Tubaro have shown that the error IEf(XT )−f(Xn T ) can be expanded in powers of 1 n , which permits to… (More)

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