CMStatistics 2021: Start Registration
View Submission - CMStatistics
Title: Local asymptotic normality property for fractional Brownian motion with measurement errors Authors:  Tetsuya Takabatake - Hiroshima University (Japan) [presenting]
Abstract: The aim is to prove a Local Asymptotic Normality (LAN) property for a fractional Brownian motion (fBm) observed at equidistant time-points in the presence of measurement errors given by some Gaussian moving average processes. We will show that the LAN property for an fBm with measurement errors heavily depends on (1) a limit of the ratio between the variances of the increments of fBm and measurement errors when the sample size goes to infinity, (2) an asymptotic behavior of the ratio between spectral density functions of the increments of fBm and measurement errors at the origin.