Dai Taguchi

TL;DR: The rate of strong convergence where the possibly discontinuous drift coefficient satisfies a one-sided Lipschitz condition and the diffusion coefficient is Holder continuous is provided.

TL;DR: In this paper, the Euler-Maruyama approximation for multi-dimensional stochastic differential equations with irregular coefficients was considered and the rate of strong convergence was shown to be linear with respect to the one-sided Lipschitz condition.

TL;DR: In this paper, the strong rates of the Euler-Maruyama approximation for one dimensional stochastic differential equations whose drift coefficient may be neither continuous nor one-sided Lipschitz and diffusion coefficient is Holder continuous were studied.

TL;DR: In this paper, the strong convergence for the Euler-Maruyama approximation of a class of stochastic differential equations whose both drift and diffusion coefficients are possibly discontinuous was studied.

TL;DR: In this article, the authors considered a numerical approximation of the stochastic differential equation (SDE) X t = x 0 + ∫ 0 t b ( s, X s ) d s + L t, x 0 ∈ R d, t ∈ [ 0, T ], where the drift coefficient b : [ 0, T ] × R d → R d is Holder continuous in both time and space variables and the noise L = (L t ) 0 ≤ t ≤ T is a d -dimensional Levy process.