The Euler Scheme for Levy Driven Stochastic Differential Equations∗
نویسندگان
چکیده
In relation with Monte-Carlo methods to solve some integro-differential equations, we study the approximation problem of IEg(XT ) by IEg(X̄n T ), where (Xt, 0 ≤ t ≤ T ) is the solution of a stochastic differential equation governed by a Lévy process (Zt), (X̄n t ) is defined by the Euler discretization scheme with step Tn . With appropriate assumptions on g(·), we show that the error IEg(XT ) − IEg(X̄n T ) can be expanded in powers of 1 n if the Lévy measure of Z has finite moments of order high enough. Otherwise the rate of convergence is slower and its speed depends on the behavior of the tails of the Lévy measure.
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