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A ratio ergodic theorem for increasing additive functionals
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  • Published: July 1986

A ratio ergodic theorem for increasing additive functionals

  • K. Bruce Erickson1 

Probability Theory and Related Fields volume 72, pages 493–504 (1986)Cite this article

Summary

Let B be a 1-dimensional Brownian motion. In this paper ratios of the form A + (t)/A - (t), where A + is the (0, ∞)-occupation time functional of B and A -is a local time integral of an infinite (but locally finite) measure m with support in (-∞, 0), are studied. Conditions on m are given which ensure that such a ratio will be unbounded a.s. (or go to zero a.s.) as t»∞.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Washington, 98195, Seattle, WA, USA

    K. Bruce Erickson

Authors
  1. K. Bruce Erickson
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Additional information

The work was supported in part by a grant from the National Science Foundation.

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Cite this article

Erickson, K.B. A ratio ergodic theorem for increasing additive functionals. Probab. Th. Rel. Fields 72, 493–504 (1986). https://doi.org/10.1007/BF00344717

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  • Received: 15 July 1984

  • Issue Date: July 1986

  • DOI: https://doi.org/10.1007/BF00344717

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Keywords

  • Stochastic Process
  • Brownian Motion
  • Probability Theory
  • Statistical Theory
  • Local Time
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