Convergence of the tamed-Euler-Maruyama method for SDEs with discontinuous and polynomially growing drift

arXiv2212.08839MaRDI QIDQ6508232

Michaela Szölgyenyi, Kathrin Spendier

Abstract: Numerical methods for SDEs with irregular coefficients are intensively studied in the literature, with different types of irregularities usually being attacked separately. In this paper we combine two different types of irregularities: polynomially growing drift coefficients and discontinuous drift coefficients. For SDEs that suffer from both irregularities we prove strong convergence of order $1/2$ of the tamed-Euler-Maruyama scheme from [Hutzenthaler, M., Jentzen, A., and Kloeden, P. E., The Annals of Applied Probability, 22(4):1611-1641, 2012].

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Numerical solutions to stochastic differential and integral equations (65C30)

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