Abstract:

In this paper we study the $L^p$-convergence rate of the tamed Euler scheme for scalar stochastic differential equations (SDEs) with piecewise continuous drift coefficient. More precisely, under the assumptions that the drift coefficient is piecewise continuous and polynomially growing and that the diffusion coefficient is Lipschitz continuous and non-zero at the discontinuity points of the drift coefficient, we show that the SDE has a unique strong solution and the $L^p$-convergence order of the tamed Euler scheme is at least 1/2 for all $p \in [1,\infty)$. Moreover, a numerical example is provided to support our conclusion.

Key words: Stochastic differential equation , Drift coefficient , Tamed Euler scheme , $L^p$-convergence rate