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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), 529-536
MSC: Primary 60J65; Secondary 60G17
DOI: https://doi.org/10.1090/S0002-9939-1993-1116258-6
MathSciNet review: 1116258
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Abstract | References | Similar Articles | 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.


References [Enhancements On Off] (What's this?)

  • [1] A. N. Borodin, On the distribution of functionals of Brownian local time, LOMI preprint E-4-35, 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), 205-233. MR 0026274 (10:132b)
  • [3] G. Doetsch, Introduction to the theory and application of the Laplace transformation, Springer-Verlag, 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), 22-25. (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. 189-215. 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, North-Holland, Amsterdam, 1970.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1993-1116258-6
Keywords: Wiener process, almost sure behavior
Article copyright: © Copyright 1993 American Mathematical Society

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