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On the future infima of some transient processes
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  • Published: September 1994

On the future infima of some transient processes

  • Davar Khoshnevisan1,
  • Thomas M. Lewis2 &
  • Wenbo V. Li3 

Probability Theory and Related Fields volume 99, pages 337–360 (1994)Cite this article

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Summary

Let (X(t), t∈S) be a real-valued stochastic process with ℙ(X(0)=0)=1 and\(\mathbb{P} (\mathop {\lim }\limits_{t \to \infty } X(t) = \infty ) = 1\). In this paper we are interested in the reluctance of such a process to tend to infinity. This entails determining the rate of escape of the associated process\((\mathop {\inf }\limits_{s\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{ \geqslant } t} X(s), t \in S)\), the so-calledfuture infima process.

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Author information

Authors and Affiliations

  1. Department of Mathematics GN-50, University of Washington, 98195, Seattle, WA, USA

    Davar Khoshnevisan

  2. Department of Mathematics, Furman University, 29613, Greenville, SC, USA

    Thomas M. Lewis

  3. Department of Math. Sciences, University of Delaware, 19716, Newark, DE, USA

    Wenbo V. Li

Authors
  1. Davar Khoshnevisan
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  2. Thomas M. Lewis
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  3. Wenbo V. Li
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Additional information

Research supported by NSF grant DMS-9122242

Research supported by NSF grants DMS-9122242 and DMS-9024961

Research supported by NSF grants DMS-9024961 and DMS-8901545

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Cite this article

Khoshnevisan, D., Lewis, T.M. & Li, W.V. On the future infima of some transient processes. Probab. Th. Rel. Fields 99, 337–360 (1994). https://doi.org/10.1007/BF01199896

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  • Received: 30 November 1993

  • Revised: 20 January 1994

  • Issue Date: September 1994

  • DOI: https://doi.org/10.1007/BF01199896

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Mathematics Subject Classification (1990)

  • 60J65
  • 60G17
  • 60J15
  • 60F05
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