Fractional Diffusion Bridges
Probability
2025-12-02 v1
Abstract
Consider ``stochastic differential equations" driven by fractional Brownian motion with Hurst parameter H (1/4 <H< 1). Their solutions are sometimes called fractional diffusion processes. The main purpose of this paper is conditioning these processes to reach a given terminal point. We call the conditioned processes fractional diffusion bridges. Our main tool for mathematically rigorous conditioning is quasi-sure analysis, which is a potential theoretic part of Malliavin calculus. We also prove a small-noise large deviation principle of Freidlin-Wentzell type for scaled fractional diffusion bridges under a mild ellipticity assumption on the coefficient vector fields.
Cite
@article{arxiv.2512.01197,
title = {Fractional Diffusion Bridges},
author = {Yuzuru Inahama},
journal= {arXiv preprint arXiv:2512.01197},
year = {2025}
}
Comments
46 pages. No figures