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Theory of Probability and Mathematical Statistics

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Local properties of a multifractional stable field


Author: Georgiy Shevchenko
Translated by: The author
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 85 (2011).
Journal: Theor. Probability and Math. Statist. 85 (2012), 159-168
MSC (2010): Primary 60G52, 60G17; Secondary 60G22, 60G18
DOI: https://doi.org/10.1090/S0094-9000-2013-00882-5
Published electronically: January 14, 2013
MathSciNet review: 2933711
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Abstract: An anisotropic harmonizable multifractional stable field is defined. Its continuity is proved. Existence and square integrability of local time are established. It is proved that the local time is jointly continuous in the Gaussian case.


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Additional Information

Georgiy Shevchenko
Affiliation: Department of Probability Theory, Statistics and Actuarial Mathematics, Mechanics and Mathematics Faculty, Kyiv National Taras Shevchenko University, 60 Volodymyrska, 01601 Kyiv, Ukraine
Email: zhora@univ.kiev.ua

DOI: https://doi.org/10.1090/S0094-9000-2013-00882-5
Keywords: Stable process, harmonizable process, multifractionality, local time, local non-determinism
Published electronically: January 14, 2013
Additional Notes: The author is grateful to the European commission for support of research within the “Marie Curie Actions” program, grant PIRSES-GA-2008-230804
Article copyright: © Copyright 2013 American Mathematical Society

American Mathematical Society