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Limit theorems for functions of a fractional Brownian motion
A. V. Savitskii Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Abstract:
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.
Keywords:
random processes, probability theory, fractional Brownian motion, Hurst exponent, limit theorems.
Received: 15.10.2019 Accepted: 14.11.2019
Citation:
A. V. Savitskii, “Limit theorems for functions of a fractional Brownian motion”, Teor. Veroyatnost. i Primenen., 65:1 (2020), 42–62; Theory Probab. Appl., 65:1 (2020), 32–48
Linking options:
https://www.mathnet.ru/eng/tvp5365https://doi.org/10.4213/tvp5365 https://www.mathnet.ru/eng/tvp/v65/i1/p42
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