This paper aims to investigate the tamed Euler method for the random periodic solution of semilinear SDEs with one-sided Lipschitz coefficient.We introduce a novel approach to analyze mean-square error bounds of the n...This paper aims to investigate the tamed Euler method for the random periodic solution of semilinear SDEs with one-sided Lipschitz coefficient.We introduce a novel approach to analyze mean-square error bounds of the novel schemes,without relying on a priori high-order moment bound of the numerical approximation.The expected order-one mean square convergence is attained for the proposed scheme.Moreover,a numerical example is presented to verify our theoretical analysis.展开更多
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 d...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∈[1,∞).Moreover,a numerical example is provided to support our conclusion.展开更多
基金supported by the National Natural Science Foundation of China(Nos.12471394,12371417)Natural Science Foundation of Changsha(No.kq2502101)。
文摘This paper aims to investigate the tamed Euler method for the random periodic solution of semilinear SDEs with one-sided Lipschitz coefficient.We introduce a novel approach to analyze mean-square error bounds of the novel schemes,without relying on a priori high-order moment bound of the numerical approximation.The expected order-one mean square convergence is attained for the proposed scheme.Moreover,a numerical example is presented to verify our theoretical analysis.
基金supported by the National Natural Science Foundation of China(Nos.12371417,11971488)。
文摘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∈[1,∞).Moreover,a numerical example is provided to support our conclusion.
