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Properties of trajectories of a multifractional Rosenblatt process
Author:
Georgiĭ Shevchenko
Translated by:
N. Semenov
Original publication:
Teoriya Imovirnostei ta Matematichna Statistika, tom 83 (2010).
Journal:
Theor. Probability and Math. Statist. 83 (2011), 163-173
MSC (2010):
Primary 60G22; Secondary 60J55, 60B10
Posted:
February 2, 2012
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Additional Information
Abstract: A Rosenblatt process and its multifractional counterpart are considered. For a multifractional Rosenblatt process, we investigate the local properties of its trajectories, namely the continuity and localizability. We prove the existence of square integrable local times for both processes.
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Additional Information
Georgiĭ Shevchenko
Affiliation:
Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 2, Kiev 03127, Ukraine
Email:
zhora@univ.kiev.ua
DOI:
http://dx.doi.org/10.1090/S0094-9000-2012-00849-1
PII:
S 0094-9000(2012)00849-1
Keywords:
Rosenblatt process,
multiple stochastic integral,
local time,
localizability,
fractional Brownian motion
Received by editor(s):
28/AUG/2010
Posted:
February 2, 2012
Additional Notes:
The author is grateful to the European Commission for a support in the framework of the program “Marie Curie Actions”, Grant # PIRSES-GA-2008-230804
Article copyright:
© Copyright 2012 American Mathematical Society
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