Asymptotic behavior of mixed power variations and statistical estimation in mixed models

TL;DR

This paper studies the asymptotic properties of mixed power variations involving Wiener and fractional Brownian motions, and uses these results to develop consistent parameter estimators in mixed models.

Contribution

It provides new asymptotic analysis of mixed power variations and introduces strongly consistent estimators for parameters in mixed stochastic models.

Findings

Asymptotic behavior of mixed power variations characterized

Strongly consistent parameter estimators constructed

Results applicable to models combining Wiener and fractional Brownian motions

Abstract

We obtain results on both weak and almost sure asymptotic behaviour of power variations of a linear combination of independent Wiener process and fractional Brownian motion. These results are used to construct strongly consistent parameter estimators in mixed models.