Fractional Diffusion Bridges

Fuente: arXiv
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Main Author: Inahama, Yuzuru
Format: Preprint
Published: 2025
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_version_ 1866908683702632448
author Inahama, Yuzuru
author_facet Inahama, Yuzuru
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2512_01197
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Fractional Diffusion Bridges
Inahama, Yuzuru
Probability
60L20, 60H07, 60G22, 60F10
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.
title Fractional Diffusion Bridges
topic Probability
60L20, 60H07, 60G22, 60F10
url https://arxiv.org/abs/2512.01197