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Strong convergence of the tamed Euler method for stochastic differential equations with piecewise continuous arguments and Poisson jumps

Yang Huizi (Department of Mathematics, Harbin Institute of Technology, Harbin, PR China)
Song Minghui (Department of Mathematics, Harbin Institute of Technology, Harbin, PR China)
Liu Mingzhu (Department of Mathematics, Harbin Institute of Technology, Harbin, PR China)
Wang Hong (Department of Mathematics, Harbin Institute of Technology, Harbin, PR China)

In the present work, the tamed Euler method is proven to be strongly convergent for stochastic differential equations with piecewise continuous arguments and Poisson jumps, where the diffusion and jump coefficients are globally Lipschitz continuous, the drift coefficient is one-sided Lipschitz continuous, and its derivative demonstrates an at most polynomial growth. Moreover, the convergence rate is obtained.

Keywords: Stochastic differential equations with piecewise continuous arguments and Poisson jumps(SEPCAwjs), Tamed Eulermethod, Convergence