Rough functional Itô formula

We prove a rough Itô formula for path-dependent functionals of α -Hölder continuous paths for α ∈ ( 0 , 1 ) . Our approach combines the sewing lemma and a Taylor approximation in terms of path-dependent derivatives.

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Publication Details

Journal
Stochastic Processes and their Applications
Published
2025-11-10
DOI
https://doi.org/10.1016/j.spa.2025.104826
Primary Topic
Mathematical Dynamics and Fractals
Type
article
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article

Rough functional Itô formula

Franziska Bielert
Stochastic Processes and their Applications
Mathematical Dynamics and Fractals
article

Rough functional Itô formula

Franziska Bielert
article en

Abstract

We prove a rough Itô formula for path-dependent functionals of α -Hölder continuous paths for α ∈ ( 0 , 1 ) . Our approach combines the sewing lemma and a Taylor approximation in terms of path-dependent derivatives.

Stochastic Processes and their ApplicationsVol. 192
Technische Universität Berlin (DE)
Openalex Percentile: Top 60%
Mathematical Dynamics and Fractals
DOIOpen Access PDFOpenAlex
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Rough functional Itô formula — Franziska Bielert · Stochastic Processes and their Applications (2025) | TGRS Research Map | TGRS