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Brownian motion and random walk perturbed at extrema
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  • Published: March 1999

Brownian motion and random walk perturbed at extrema

  • Burgess Davis1 

Probability Theory and Related Fields volume 113, pages 501–518 (1999)Cite this article

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Abstract

Let b t be Brownian motion. We show there is a unique adapted process x t which satisfies dx t = db t except when x t is at a maximum or a minimum, when it receives a push, the magnitudes and directions of the pushes being the parameters of the process. For some ranges of the parameters this is already known. We show that if a random walk close to b t is perturbed properly, its paths are close to those of x t .

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Authors and Affiliations

  1. Statistics Department, Mathematical Sciences Buildings, West Lafayette, IN 47907-1399, USA. e-mail:Purdue University, bdavis@state.purdue.edu, , , , , , US

    Burgess Davis

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  1. Burgess Davis
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Received: 15 October 1997 / Revised version: 18 May 1998

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Davis, B. Brownian motion and random walk perturbed at extrema. Probab Theory Relat Fields 113, 501–518 (1999). https://doi.org/10.1007/s004400050215

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  • Issue Date: March 1999

  • DOI: https://doi.org/10.1007/s004400050215

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  • Mathematics Subject Classification (1991): 60F05, 60J15, 60J65, 82C41
  • Key words and phrases: Reinforced random walk – Perturbed Brownian motion
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