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

## TL;DR

This paper introduces a class of self-similar Gaussian processes, characterizes their small scale limits, and applies these findings to estimation problems, encompassing several well-known processes.

## Contribution

It provides necessary and sufficient conditions for self-similar Gaussian processes to have unique small scale limits, expanding understanding of their asymptotic behavior.

## Key findings

- Characterization of small scale limits for the class
- Conditions for uniqueness of limits in Skorokhod space
- Application to estimation problems

## 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.