Itô formula for reduced rough paths

Fuente: arXiv
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Main Authors: Li, Nannan, Gao, Xing
Format: Preprint
Published: 2025
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author Li, Nannan
Gao, Xing
author_facet Li, Nannan
Gao, Xing
contents The Itô formula, also known as the change-of-variables formula, is a cornerstone of Itô stochastic calculus. Over time, this formula has been extended to apply to random processes for which classical calculus is insufficient. Since every random process exhibits some degree of regularity, rough path theory provides a natural framework for treating them uniformly. In this paper, we extend the Itô formula for reduced rough paths, broadening the range of roughness from the previously known case $\frac{1}{3} < α\leq \frac{1}{2}$ to the more singular regime $\frac{1}{4} < α\leq \frac{1}{3}$.
format Preprint
id arxiv_https___arxiv_org_abs_2509_17342
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Itô formula for reduced rough paths
Li, Nannan
Gao, Xing
Probability
60L20, 60H99, 34K50
The Itô formula, also known as the change-of-variables formula, is a cornerstone of Itô stochastic calculus. Over time, this formula has been extended to apply to random processes for which classical calculus is insufficient. Since every random process exhibits some degree of regularity, rough path theory provides a natural framework for treating them uniformly. In this paper, we extend the Itô formula for reduced rough paths, broadening the range of roughness from the previously known case $\frac{1}{3} < α\leq \frac{1}{2}$ to the more singular regime $\frac{1}{4} < α\leq \frac{1}{3}$.
title Itô formula for reduced rough paths
topic Probability
60L20, 60H99, 34K50
url https://arxiv.org/abs/2509.17342