Rough Volterra equations 2: convolutional generalized integrals
Samy Tindel (IECN), Aur\'elien Deya (IECN)
TL;DR
This paper develops a novel approach to solving Volterra equations driven by irregular signals using a generalized rough path theory with exponential weights, with applications to fractional Brownian motion.
Contribution
It introduces a new method for solving Volterra equations with irregular signals via a convolutional rough path framework, extending existing theories.
Findings
Successfully defines and solves Volterra equations with irregular signals
Extends rough path theory to include exponential weighting
Applies the framework to fractional Brownian motion with Hurst > 1/3
Abstract
We define and solve Volterra equations driven by an irregular signal, by means of a variant of the rough path theory allowing to handle generalized integrals weighted by an exponential coefficient. The results are applied to the fractional Brownian motion with Hurst coefficient greater than 1/3
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Taxonomy
TopicsStochastic processes and financial applications · Fractional Differential Equations Solutions · Fluid Dynamics and Turbulent Flows