arXiv subjects

Tsukasa Moritoki

Publications and source records attributed to Tsukasa Moritoki.

2 recordsLinked to original sources

arXiv2026

Strong rate of convergence for the Euler-Maruyama scheme of additive fractional SDEs with Lipschitz drift

We study the strong convergence rate of the Euler-Maruyama scheme for additive stochastic differential equations driven by a fractional Brownian motion with Hurst parameter $H \in (0,1)$. Assuming the drift coefficient to be Lipschitz continuous, we show that the rate is $1$ if $H \in (1/2,1)$, and $1/2+H-\varepsilon$, for any $\varepsilon>0$, if $H \in (0,1/2]$. The main ingredient is a shifted stochastic sewing argument, which exploits the conditional Gaussian structure of fractional Brownian motion to control the noise discretization error.

math.PR↗

arXiv2026

Strong rate of convergence for the Euler--Maruyama scheme of SDEs with unbounded H\"older continuous drift coefficient

In this paper, we provide the strong rate of convergence for the Euler--Maruyama scheme for multi-dimensional stochastic differential equations with uniformly locally (unbounded) H\"older continuous drift and multiplicative noise. Our technique is based on It\^o--Tanaka trick (Zvonkin transformation) for unbounded drift. Moreover, in order to apply the stochastic sewing lemma, we use the heat kernel estimate for the density function of the Euler--Maruyama scheme.

math.PR↗