The time spent by the Wiener process in a narrow tube before leaving a wide tube
Authors:
Antónia Földes and Madan L. Puri
Journal:
Proc. Amer. Math. Soc. 117 (1993), 529536
MSC:
Primary 60J65; Secondary 60G17
MathSciNet review:
1116258
Fulltext PDF Free Access
Abstract 
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Additional Information
Abstract: The almost sure behavior of the time spent by the Wiener process in a "small interval" before first leaving a "bigger interval" is investigated.
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 [1]
 A. N. Borodin, On the distribution of functionals of Brownian local time, LOMI preprint E435, U.S.S.R. Academy of Sciences, Steklov Mathematical Institute, Leningrad Department, 1985.
 [2]
 K. L. Chung, On the maximum partial sums of sequences of independent random variables, Trans. Amer. Math. Soc. 64 (1948), 205233. MR 0026274 (10:132b)
 [3]
 G. Doetsch, Introduction to the theory and application of the Laplace transformation, SpringerVerlag, New York, Heidelberg, and Berlin, 1970. MR 0344810 (49:9549)
 [4]
 I. S. Gradshteyn and I. M. Ryzhik, Table of integrals, series and products, Academic Press, New York, 1980.
 [5]
 R. Z. Hasminskiĭ, Probability distributions for functionals of the trajectories of diffusion type random processes, Dokl. Akad. Nauk SSSR 100 (1985), 2225. (Russian)
 [6]
 M. Kac, On some connections between probability theory and differential and integral equations, Proc. Second Berkeley Sympos. Math. Statist, and Prob. 1950, Univ. of California Press, Berkeley and Los Angeles, pp. 189215. MR 0045333 (13:568b)
 [7]
 F. B. Knight, Essentials of Brownian motion and diffusion, Amer. Math. Soc., Providence, RI, 1981. MR 613983 (82m:60098)
 [8]
 A. Rényi, Probability theory, NorthHolland, Amsterdam, 1970.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939199311162586
PII:
S 00029939(1993)11162586
Keywords:
Wiener process,
almost sure behavior
Article copyright:
© Copyright 1993
American Mathematical Society
