# A Stochastic Calculus for Rosenblatt Processes

## TL;DR

This paper develops a stochastic calculus framework for Rosenblatt processes, similar to Itô calculus, enabling analysis of functionals and applications involving Rosenblatt noise.

## Contribution

It introduces a stochastic calculus for Rosenblatt processes, expanding tools for analyzing non-Gaussian processes in stochastic analysis.

## Key findings

- Derived Itô-type expressions for Rosenblatt processes
- Established a stochastic chain rule for Rosenblatt functionals
- Analyzed applications to Rosenblatt noise problems

## Abstract

A stochastic calculus is given for processes described by stochastic integrals with respect to fractional Brownian motions and Rosenblatt processes somewhat analogous to the stochastic calculus for It\^{o} processes. These processes for this stochastic calculus arise naturally from a stochastic chain rule for functionals of Rosenblatt processes; and some It\^{o}-type expressions are given here. Furthermore, there is some analysis of these results for their applications to problems using Rosenblatt noise.