Functional law of the iterated logarithm type for a skew Brownian motion
Author:
I. H. Krykun
Translated by:
S. Kvasko
Journal:
Theor. Probability and Math. Statist. 87 (2013), 79-98
MSC (2000):
Primary 60F10; Secondary 60F17
DOI:
https://doi.org/10.1090/S0094-9000-2014-00906-0
Published electronically:
March 21, 2014
MathSciNet review:
3241448
Full-text PDF Free Access
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Additional Information
Abstract: The functional law of the iterated logarithm is proved for a skew Brownian motion.
References
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- V. Strassen, An invariance principle for the law of the iterated logarithm, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 3 (1964), 211–226 (1964). MR 175194, DOI https://doi.org/10.1007/BF00534910
References
- A. V. Bulinskiĭ, A new variant of the functional law of the iterated logarithm, Teor. Veroyatnost. i Primenen. 25 (1980), no. 3, 502–512; English transl. in Theory Probab. Appl. 25 (1980), no. 3, 493–503. MR 582580 (82f:60066)
- A. D. Wentzell and M. I. Freidlin, Random Perturbations of Dynamical Systems, “Nauka”, Moscow, 1979; English transl., Springer-Verlag, New York, 1984. MR 722136 (85a:60064)
- I. I. Gikhman and A. V. Skorokhod, Stochastic Differential Equations and their Applications, “Naukova Dumka”, Kiev, 1982. (Russian) MR 678374 (84j:60003)
- S. Ya. Makhno, A limit theorem for stochastic equations with local time, Teor. Imovir. Mat. Stat. 64 (2001), 106–109; English transl. in Theory Probab. Math. Statist. 64 (2002), 123–127. MR 1922958 (2003h:60090)
- A. N. Shiryaev, Probability, “Nauka”, Moscow, 1980; English transl., Springer-Verlag, New York, 1996. MR 609521 (82d:60002)
- T. S. Chiang and S. J. Sheu, Small perturbations of diffusions in inhomogeneous media, Ann. Inst. Henri Poincaré 38 (2002), no. 2, 285–318. MR 1899455 (2003b:60084)
- H. J. Engelbert and W. Schmidt, Strong Markov continuous local martingales and solutions of one-dimensional stochastic differential equations, III, Math. Nachr. 151 (1991), no. 1, 149–197. MR 1121203 (92m:60044)
- J. M. Harrison and L. A. Shepp, On skew Brownian motion, Ann. Probab. 9 (1981), no. 2, 309–313. MR 606993 (82j:60144)
- K. Itô and H. McKean, Brownian motions on a half line, Illinois J. Math. 7 (1963), no. 2, 181–231. MR 0154338 (27:4287)
- J. F. Le Gall, One-dimensional stochastic equations involving the local times of the unknown process, Lect. Notes Math. 1095 (1983), 51–82. MR 777514 (86g:60071)
- S. Ya. Makhno, Functional iterated logarithm law for stochastic equations, Stoch. Stoch. Reports 70 (2000), 221–239. MR 1800957 (2001j:60055)
- S. Nakao, On the pathwise uniqueness of solutions of one dimensional stochastic differential equations, Osaka J. Math. 9 (1972), no. 3, 513–518. MR 0326840 (48:5182)
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Additional Information
I. H. Krykun
Affiliation:
Department of Probability Theory and Mathematical Statistics, Institute for Applied Mathematics and Mechanics, National Academy of Science of Ukraine, Luxemburg Street, 74, Donetsk, 83114, Ukraine
Email:
ikrykun@iamm.ac.donetsk.ua
Keywords:
Stochastic equations,
local time,
large deviation principle,
functional law of the iterated logarithm
Received by editor(s):
November 9, 2010
Published electronically:
March 21, 2014
Article copyright:
© Copyright 2014
American Mathematical Society
