White noise based stochastic calculus associated with a class of Gaussian processes

TL;DR

This paper develops a white noise space framework for stochastic calculus involving a class of stationary increment Gaussian processes, including defining integrals and proving an Ito formula within the Kondratiev space setting.

Contribution

It introduces a novel white noise based stochastic calculus for Gaussian processes with stationary increments, extending the theory to Kondratiev spaces and establishing an Ito formula.

Findings

Defined stochastic integrals for Gaussian processes in white noise space

Proved an Ito formula in the Kondratiev space setting

Extended stochastic calculus to a new class of Gaussian processes

Abstract

Using the white noise space setting, we define and study stochastic integrals with respect to a class of stationary increment Gaussian processes. We focus mainly on continuous functions with values in the Kondratiev space of stochastic distributions, where use is made of the topology of nuclear spaces. We also prove an associated Ito formula.