Decomposition and limit theorems for a class of self-similar Gaussian processes

2015/08/26 by Daniel Harnett, David Nualart, Harnett, Daniel +1
Economics, Econometrics and Finance · #60F05 #60G18 #60H07 #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1508.06641

openalex publication_date 2015/08/26 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28

Abstract

We introduce a new class of self-similar Gaussian stochastic processes, where the covariance is defined in terms of a fractional Brownian motion and another Gaussian process. A special case is the solution in time to the fractional-colored stochastic heat equation described in Tudor (2013). We prove that the process can be decomposed into a fractional Brownian motion (with a different parameter than the one that defines the covariance), and a Gaussian process first described in Lei and Nualart (2008). The component processes can be expressed as stochastic integrals with respect to the Brownian sheet. We then prove a central limit theorem about the Hermite variations of the process.

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