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
MathSciNet review:
3364127
Full-text PDF Free Access
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
