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Theory of Probability and Mathematical Statistics
Theory of Probability and Mathematical Statistics
ISSN 1547-7363(online) ISSN 0094-9000(print)

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
Published electronically: February 2, 2012
MathSciNet review: 2768856
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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): August 28, 2010
Published electronically: 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