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On the character of convergence to Brownian local time. I
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  • Published: June 1986

On the character of convergence to Brownian local time. I

  • A. N. Borodin1 

Probability Theory and Related Fields volume 72, pages 231–250 (1986)Cite this article

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Summary

Many results are known about the convergence of some processes to Brownian local time. Among such processes are the process of “occupation times” of Brownian motion, the number of downcrossings of Brownian motion over smaller and smaller intervals before timet, the number of visits of the recurrent integer-valued random walk to some point duringn steps and others. In this paper we consider the asymptotic behaviour of the differences between Brownian local time and some of the processes which converge to it.

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Authors and Affiliations

  1. Leningrad Branch Steklov Institute of Mathematics Academy of Sciences of the USSR, Fontanka 27, 191011, Leningrad, USSR

    A. N. Borodin

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  1. A. N. Borodin
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Borodin, A.N. On the character of convergence to Brownian local time. I. Probab. Th. Rel. Fields 72, 231–250 (1986). https://doi.org/10.1007/BF00699105

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  • Received: 25 June 1984

  • Accepted: 08 November 1985

  • Issue Date: June 1986

  • DOI: https://doi.org/10.1007/BF00699105

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Keywords

  • Stochastic Process
  • Brownian Motion
  • Asymptotic Behaviour
  • Random Walk
  • Probability Theory
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