Limit theorems for functions of a fractional Brownian motionстатья
Информация о цитировании статьи получена из
Scopus
Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 15 февраля 2024 г.
Аннотация:Sample statistics of samples from a fractional Brownian motion with Hurst exponent H, and in particular, autocovariance statistics, are considered. Two statistics characterizing the covariate dependence between the increments of this process are studied; in particular, their asymptotic properties and the limit distributions are examined. Each of the statistics is shown to converge almost everywhere; their limits are evaluated. It is found that these statistics have different limit distributions depending on the value of H. A complete description of these distributions in terms of semi-invariants is put forward.