Pathwise Regularity and Small-Time Asymptotics for Stochastic Processes via Rough Path Techniques

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Autori principali: Revista, Zen, MATH, 10
Natura: Recurso digital
Pubblicazione: Zenodo 2025
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author Revista, Zen
MATH, 10
author_facet Revista, Zen
MATH, 10
contents This paper investigates the pathwise regularity and small-time asymptotics of stochastic processes using the framework of rough path theory. We focus on processes driven by fractional Brownian motion and other Gaussian processes with Hölder regularity less than 1/2. The rough path approach allows us to define stochastic integrals pathwise and to establish regularity results for solutions of stochastic differential equations (SDEs) driven by these processes. We derive small-time expansions for the solutions of SDEs and analyze the convergence rates. The results are obtained by constructing suitable rough path lifts of the driving processes and applying estimates from rough path theory. We also provide examples and applications of the theory to stochastic volatility models and other areas of quantitative finance.
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spellingShingle Pathwise Regularity and Small-Time Asymptotics for Stochastic Processes via Rough Path Techniques
Revista, Zen
MATH, 10
This paper investigates the pathwise regularity and small-time asymptotics of stochastic processes using the framework of rough path theory. We focus on processes driven by fractional Brownian motion and other Gaussian processes with Hölder regularity less than 1/2. The rough path approach allows us to define stochastic integrals pathwise and to establish regularity results for solutions of stochastic differential equations (SDEs) driven by these processes. We derive small-time expansions for the solutions of SDEs and analyze the convergence rates. The results are obtained by constructing suitable rough path lifts of the driving processes and applying estimates from rough path theory. We also provide examples and applications of the theory to stochastic volatility models and other areas of quantitative finance.
title Pathwise Regularity and Small-Time Asymptotics for Stochastic Processes via Rough Path Techniques
url https://doi.org/10.5281/zenodo.17830746