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Theoretical and Mathematical Physics

, Volume 90, Issue 3, pp 219–241 | Cite as

Distribution of some functionals of the integral of a random walk

  • Ya. G. Sinai
Article

Abstract

The asymptotic behavior of the probabilities associated with the first crossing of a straight line or parabola by the integral of a Brownian curve is studied.

Keywords

Asymptotic Behavior Random Walk Brownian Curve 
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References

  1. 1.
    A. Ya. Khinchin,Continued Fractions [in Russian], Nauka, Moscow (1978).Google Scholar
  2. 2.
    W. Feller,An Introduction to Probability Theory and its Applications, Vol. 1, Wiley, New York (1950).Google Scholar
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    W. Feller,An Introduction to Probability Theory and its Applications, Vol. 2, Wiley, New York (1966).Google Scholar
  4. 4.
    E. Sparre-Andersen, “On the fluctuations of sums of random variables,”Math. Scand.,1, 263 (1953);2, 195 (1954).Google Scholar

Copyright information

© Plenum Publishing Corporation 1992

Authors and Affiliations

  • Ya. G. Sinai

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