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

 

Laws of iterated logarithm for stochastic integrals of generalized sub-Gaussian processes


Authors: A. Castellucci and R. Giuliano Antonini
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 73 (2005).
Journal: Theor. Probability and Math. Statist. 73 (2006), 47-56
MSC (2000): Primary 60F15; Secondary 60G44
Published electronically: January 17, 2007
MathSciNet review: 2213840
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Abstract | References | Similar Articles | Additional Information

Abstract: We study the behavior of $ \phi$-sub-Gaussian martingales $ (M_t)_{t>0}$ as $ t \to 0$. Applications are given to the stochastic integral of a particular kind of process and to the double stochastic integral of it with respect to two independent Brownian motions.


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Additional Information

A. Castellucci
Affiliation: Dip. di Matematica, Università di Pisa, via F. Buonarroti 2, 56100 Pisa, Italy
Email: castellucci@mail.dm.unipi.it

R. Giuliano Antonini
Affiliation: Dip. di Matematica, Università di Pisa, via F. Buonarroti 2, 56100 Pisa, Italy
Email: giuliano@dm.unipi.it

DOI: http://dx.doi.org/10.1090/S0094-9000-07-00680-1
PII: S 0094-9000(07)00680-1
Keywords: Continuous time martingale, generalized sub-Gaussian process, iterated logarithm law, Brownian motion, double stochastic integral, L\'evy area process
Received by editor(s): July 30, 2004
Published electronically: January 17, 2007
Article copyright: © Copyright 2007 American Mathematical Society