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Theory of Probability and Mathematical Statistics

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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
Published electronically: February 4, 2016
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Abstract: Two theorems describing the asymptotic behavior of integral functionals of multidimensional self-similar random fields are proved. For a $ d$-dimensional fractional Brownian field depending on $ N$ parameters, a theorem on the convergence of the integral mean-type functional is established. The weak convergence of an integral functional of a $ d$-dimensional anisotropic self-similar random field with $ N$ 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

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

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