On stochastic integration for volatility modulated Brownian-driven Volterra processes via white noise analysis

TL;DR

This paper extends the stochastic integration framework for volatility modulated Volterra processes driven by Brownian motion, utilizing white noise analysis to handle generalized processes and introducing a novel volatility modulation method via the Wick product.

Contribution

It generalizes the integration theory to the space of Potthoff-Timpel distributions and introduces a new volatility modulation technique using the Wick product.

Findings

Provided sufficient conditions for integrability of generalized processes.

Discussed regularity and properties of the stochastic integral.

Introduced a new volatility modulation method through the Wick product.

Abstract

This paper generalizes the integration theory for volatility modulated Brownian-driven Volterra processes onto the space G* of Potthoff-Timpel distributions. Sufficient conditions for integrability of generalized processes are given, regularity results and properties of the integral are discussed. We introduce a new volatility modulation method through the Wick product and discuss its relation to the pointwise-multiplied volatility model.