arXiv subjects

Teodor Holland

Publications and source records attributed to Teodor Holland.

2 recordsLinked to original sources

arXiv2024

Regularisation by multiplicative noise for reaction-diffusion equations

We consider the stochastic reaction-diffusion equation in $1+1$ dimensions driven by multiplicative space-time white noise, with a distributional drift belonging to a Besov-Hölder space with any regularity index larger than $-1$. We assume that the diffusion coefficient is a regular function which is bounded away from zero. By using a combination of stochastic sewing techniques and Malliavin calculus, we show that the equation admits a unique solution.

math.PR↗

arXiv2022

A note on the weak rate of convergence for the Euler-Maruyama scheme with Hölder drift

We consider SDEs with bounded and $α$-Hölder continuous drift, with $α\in (0,1)$, driven by multiplicative noise. We show that under sufficient conditions on the diffusion matrix, which guarantee the existence of a unique strong solution, the weak rate of convergence for the Euler-Maruyama scheme is almost $(1+α)/2$. The present paper forms part of the author's master's thesis.

math.PR↗