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The Codimension of the Zeros of a Stable Process in Random Scenery

Part of the Lecture Notes in Mathematics book series (SEMPROBAB,volume 1832)

Abstract

We show that for any α∈(1,2], the (stochastic) codimension of the zeros of an α-stable process in random scenery is identically 1-(2α)-1. As an immediate consequence, we deduce that the Hausdorff dimension of the zeros of the latter process is almost surely equal to (2α)-1. This solves Conjecture 5.2 of [6], thereby refining a computation of [10].

Keywords Random walk in random scenery; stochastic codimension; Hausdorff dimension.

AMS 2000 subject classification: 60K37

Keywords

  • Hausdorff Dimension
  • Fractional Brownian Motion
  • Random Variable Versus
  • Conditional Regression
  • Random Scenery

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 2003 Springer-Verlag Berlin Heidelberg

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Khoshnevisan, D. (2003). The Codimension of the Zeros of a Stable Process in Random Scenery. In: Azéma, J., Émery, M., Ledoux, M., Yor, M. (eds) Séminaire de Probabilités XXXVII. Lecture Notes in Mathematics, vol 1832. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-40004-2_9

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  • DOI: https://doi.org/10.1007/978-3-540-40004-2_9

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-20520-3

  • Online ISBN: 978-3-540-40004-2

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