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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
MathSciNet review:
2213840
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Additional information
Abstract:
We study the behavior of  -sub-Gaussian martingales  as  . 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.
References:
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- 1.
- V. V. Buldygin and Yu. V. Kozachenko, Metric Characterization of Random Variables and Random Processes, AMS, Providence, RI, 2000. MR 1743716 (2001g:60089)
- 2.
- W. Feller, An Introduction to Probability Theory and Its Applications, vol. II, Wiley, 1971. MR 0270403 (42:5292)
- 3.
- R. Giuliano Antonini and Yu. V. Kozachenko, A note on the asymptotic behavior of sequences of generalized sub-Gaussian random vectors, Random Oper. Stochastic Equations 13 (2005), 39-52. MR 2130246 (2006b:60020)
- 4.
- R. Giuliano Antonini, Yu. V. Kozachenko, and T. Nikitina, Spaces of
 -sub-Gaussian random variables, Rend. Acc. Naz. delle Scienze detta dei XL, Mem. Mat. Appl. 121 (2003), 95-124. MR 2056414 (2005f:60036) - 5.
- K. Helmes, The local law of the iterated logarithm for processes related to Lévy's stochastic area process, Studia Math. 83 (1986), 229-237. MR 850825 (87m:60096)
- 6.
- P. Lévy, Wiener's random function, and other Laplacian random functions, Proceedings of the second Berkeley Symposium on Mathematical Statistics and Probability, 1950. MR 0044774 (13:476b)
- 7.
- R. Schott, Une Loi du Logarithme itéré pour certaines intégrales stochastiques, Comptes Rendus de l'Académie des Sciences Paris 292 (1981), 295-298. MR 609071 (82c:60142)
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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:
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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