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Sample path behaviour in connection with generalized arcsine laws
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  • Published: September 1995

Sample path behaviour in connection with generalized arcsine laws

  • Jean Bertoin1 

Probability Theory and Related Fields volume 103, pages 317–327 (1995)Cite this article

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Summary

LetG=(G(t),t≧0) be the process of last passage times at some fixed point of a Markov process. The Dynkin-Lamperti theorem provides a necessary and sufficient condition forG(t)/t to converge in law ast→∞ to some non-degenerate limit (which is then a generalized arcsine law). Under this condition, we give a simple integral test that characterizes the lower-functions ofG. We obtain a similar result forA +=(A + (t),t≧0), the time spent in [0, ∞) by a real-valued diffusion process, in connection with Watanabe's recent extension of Lévy's second arcsine law.

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Authors and Affiliations

  1. Laboratoire de Probabilités (C.N.R.S.), Université Pierre et Marie Curie, tour 56-46, 4 Place Jussieu, F-75252, Paris Cedex 05, France

    Jean Bertoin

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  1. Jean Bertoin
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Bertoin, J. Sample path behaviour in connection with generalized arcsine laws. Probab. Th. Rel. Fields 103, 317–327 (1995). https://doi.org/10.1007/BF01195477

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  • Received: 19 September 1994

  • Revised: 01 March 1995

  • Issue Date: September 1995

  • DOI: https://doi.org/10.1007/BF01195477

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Mathematics Subject Classification

  • 60G17
  • 60J25
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