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The truncated Euler–Maruyama method for stochastic differential equations with piecewise continuous arguments driven by Lévy noise

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ABSTRACT This paper aims to consider stochastic differential equations with piecewise continuous arguments (SDEPCAs) driven by Lévy noise where both drift and diffusion coefficients satisfy local Lipschitz condition plus Khasminskii-type… Click to show full abstract

ABSTRACT This paper aims to consider stochastic differential equations with piecewise continuous arguments (SDEPCAs) driven by Lévy noise where both drift and diffusion coefficients satisfy local Lipschitz condition plus Khasminskii-type condition and the jump coefficient grows linearly. We present the explicit truncated Euler–Maruyama method. We study its moment boundedness and its strong convergence. Moreover, the convergence rate is shown to be close to that of the classical Euler method under additional conditions.

Keywords: driven noise; stochastic differential; differential equations; piecewise continuous; continuous arguments; equations piecewise

Journal Title: International Journal of Computer Mathematics
Year Published: 2021

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