A stochastic calculus for Rosenblatt processes

Petr Čoupek, Tyrone E. Duncan and Bozenna Pasik-Duncan

Stochastic Processes and their Applications, 2022, vol. 150, issue C, 853-885

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 Itô processes. These processes for this stochastic calculus arise naturally from a stochastic chain rule for functionals of Rosenblatt processes; and some Itô-type expressions are given here. Furthermore, there is some analysis of these results for their applications to problems using Rosenblatt noise.

Keywords: Rosenblatt process; Stochastic calculus; Itô formula; Skorokhod integral; Forward integral (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.spa.2020.01.004

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