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Large deviations for Markov processes with discontinuous statistics, II: random walks
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  • Published: June 1992

Large deviations for Markov processes with discontinuous statistics, II: random walks

  • Paul Dupuis1 &
  • Richard S. Ellis1 

Probability Theory and Related Fields volume 91, pages 153–194 (1992)Cite this article

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Summary

Letμ 1 andμ 2 be Borel probability measures on ℝd with finite moment generating functions. The main theorem in this paper proves the large deviation principle for a random walk whose transition mechanism is governed byμ 1 when the walk is in the left halfspace Λ1 = {x∈ℝd :x 1≦0} and whose transition mechanism is governed byμ 2 when the walk is in the right halfspace Λ2 = {x∈ℝd :x 1>0}. When the measuresμ 1 andμ 2 are equal, the main theorem reduces to Cramér's Theorem.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Massachusetts, 01003, Amberst, M/A, USA

    Paul Dupuis & Richard S. Ellis

Authors
  1. Paul Dupuis
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  2. Richard S. Ellis
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Additional information

This research was supported in part by a grant from the National Science Foundation (NSF-DMS-8902333)

This research was supported in part by a grant from the National Science Foundation (NSF-DMS-8901138) and in part by a Lady Davis Fellowship while visiting the Faculty of Industrial Engineering and Management at the Technion during the spring semester of 1989

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Dupuis, P., Ellis, R.S. Large deviations for Markov processes with discontinuous statistics, II: random walks. Probab. Th. Rel. Fields 91, 153–194 (1992). https://doi.org/10.1007/BF01291423

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  • Received: 05 July 1990

  • Revised: 25 May 1991

  • Issue Date: June 1992

  • DOI: https://doi.org/10.1007/BF01291423

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Keywords

  • Generate Function
  • Stochastic Process
  • Probability Measure
  • Random Walk
  • Probability Theory
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