On a covariance structure of some subset of self-similar Gaussian processes

Abstract

We introduce a class of self-similar Gaussian processes and provide sufficient and necessary conditions for a member of the class to admit a unique small scale limit in the Skorokhod space. The class includes several well known processes. An example of application to the problem of estimation is given.

References in corpus (3)

• Nonparametric quasi-maximum likelihood estimation for Gaussian locally stationary processes
• Asymptotic expansion and central limit theorem for quadratic variations of Gaussian processes
• Weighted power variation of integrals with respect to a Gaussian process

Cited by in corpus (2)

• Exact uniform modulus of continuity and Chung's LIL for the generalized fractional Brownian motion
• Self-similar Gaussian Markov processes