Asymptotic properties of integral functionals of fractional Brownian fields

Author:
V. I. Makogin

Translated by:
S. Kvasko

Original publication:
Teoriya Imovirnostei ta Matematichna Statistika, tom **91** (2014).

Journal:
Theor. Probability and Math. Statist. **91** (2015), 105-114

MSC (2010):
Primary 60J55, 60G60; Secondary 60G18

DOI:
https://doi.org/10.1090/tpms/970

Published electronically:
February 4, 2016

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Two theorems describing the asymptotic behavior of integral functionals of multidimensional self-similar random fields are proved. For a -dimensional fractional Brownian field depending on parameters, a theorem on the convergence of the integral mean-type functional is established. The weak convergence of an integral functional of a -dimensional anisotropic self-similar random field with parameters to the local time is proved under the assumption that the continuous local time exists for this field.

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Additional Information

**V. I. Makogin**

Affiliation:
Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue, 6, Kyiv 03127, Ukraine

Email:
makoginv@ukr.net

DOI:
https://doi.org/10.1090/tpms/970

Keywords:
Local time,
self-similar fields,
anisotropic fractional Brownian field

Received by editor(s):
September 30, 2014

Published electronically:
February 4, 2016

Article copyright:
© Copyright 2016
American Mathematical Society