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Self-similarity of Brownian motion and a large deviation principle for random fields on a binary tree
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  • Published: March 1994

Self-similarity of Brownian motion and a large deviation principle for random fields on a binary tree

  • Nina Gantert1 

Probability Theory and Related Fields volume 98, pages 7–20 (1994)Cite this article

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Summary

Using self-similarity of Brownian motion and its representation as a product measure on a binary tree, we construct a random sequence of probability measures which converges to the distribution of the Brownian bridge. We establish a large deviation principle for random fields on a binary tree. This leads to a class of probability measures with a certain self-similarity property. The same construction can be carried out forC[0, 1]-valued processes and we can describe, for instance, aC[0, 1]-valued Ornstein-Uhlenbeck process as a large deviation of Brownian sheet.

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Authors and Affiliations

  1. ETH Mathematikdepartment, ETH, CH-8092, Zürich, Switzerland

    Nina Gantert

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  1. Nina Gantert
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Gantert, N. Self-similarity of Brownian motion and a large deviation principle for random fields on a binary tree. Probab. Th. Rel. Fields 98, 7–20 (1994). https://doi.org/10.1007/BF01311346

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  • Received: 17 September 1991

  • Revised: 30 July 1993

  • Issue Date: March 1994

  • DOI: https://doi.org/10.1007/BF01311346

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Mathematics Subject Classifications (1991)

  • 60F10
  • 60J65
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