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

2013/01/06 by Dozzi, Marco, Mishura, Yuliya, Shevchenko, Georgiy · 1 citation
#60G15 #60G22 #62F25 #62M09 #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Probability (math.PR)

paper · doi:10.48550/arxiv.1301.0993

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.

Cited by

• Parameter estimation of integrated fractional Brownian motion

Related

• Power variations and limit theorems for stochastic processes controlled by fractional Brownian motions
• Estimation of mixed fractional stable processes using high-frequency data
• Maximum likelihood estimation for stochastic differential equations driven by a mixed fractional Brownian motion with random effects
• Asymptotic behavior of weighted power variations of fractional Brownian\n motion in Brownian time
• Rate-optimal estimation of mixed semimartingales