Theory of Probability and Mathematical Statistics

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

Author(s): A. Castellucci; R. Giuliano Antonini
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, vipusk 73 (2005).
Journal: Theor. Probability and Math. Statist. No. 73 (2006), 47-56.
MSC (2000): Primary 60F15; Secondary 60G44
Posted: January 17, 2007
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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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Retrieve articles in Theory of Probability and Mathematical Statistics with MSC (2000): 60F15, 60G44

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: 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): 30/JUL/2004
Posted: January 17, 2007
Copyright of article: Copyright 2007, American Mathematical Society

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ISSN: 1547-7363(e) 0094-9000(p)

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