Convergence of the stochastic Euler scheme for locally Lipschitz coefficients - Mathematics > Numerical AnalysisReport as inadecuate




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Abstract: Stochastic differential equations are often simulated with the Monte CarloEuler method. Convergence of this method is well understood in the case ofglobally Lipschitz continuous coefficients of the stochastic differentialequation. The important case of superlinearly growing coefficients, however,has remained an open question. The main difficulty is that numerically weakconvergence fails to hold in many cases of superlinearly growing coefficients.In this paper we overcome this difficulty and establish convergence of theMonte Carlo Euler method for a large class of one-dimensional stochasticdifferential equations whose drift functions have at most polynomial growth.



Author: Martin Hutzenthaler, Arnulf Jentzen

Source: https://arxiv.org/







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