arXiv subjects

Soma Nishino

Publications and source records attributed to Soma Nishino.

3 recordsLinked to original sources

arXiv2025

A central limit theorem for the stochastic cable equation

We study one-dimensional nonlinear stochastic cable equations driven by a multiplicative space-time white noise. Using the Malliavin-Stein method, we prove a central limit theorem for the spatial average of the solution. The convergence is established in the total variation distance with mild conditions. We also establish a functional central limit theorem with a technical assumption. Furthermore, we show that this assumption holds in a special case.

math.PR↗

arXiv2025

Construction and sample path properties of diffusion house-moving between two curves

The purpose of this paper is to introduce the construction of a stochastic process called ``diffusion house-moving'' and to explore its properties. We study the weak convergence of diffusion bridges conditioned to stay between two curves, and we refer to this limit as diffusion house-moving. Applying this weak convergence result, we give the sample path properties of diffusion house-moving.

math.PR↗

arXiv2024

Higher order integration by parts formulae for Wiener measures on a path space between two curves

We have formulated higher-order integration by parts formulae on the path space restricted between two curves, with respect to pinned/ordinary Wiener measures. The higher-order integration by parts formulae introduce nontrivial boundary terms, unlike the first-order one. Furthermore, in the process of proving these formulae, it becomes necessary to employ the construction methods of Brownian excursion and Brownian house-moving through random walk approximations. To express the integration by parts formula concisely, we introduced a notation called Symmetrization. This notation enables the rewriting of the intricate expressions of boundary terms associated with higher-order integration by parts into more concise forms. Additionally, we provided a probabilistic explanation for the boundary terms by introducing symbols based on the concept of infinitesimal probability. These efforts are aimed at fostering an intuitive understanding of the integration by parts formulae.

math.PR↗