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
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
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
Download citation
DOI: https://doi.org/10.1007/978-3-540-40004-2_9
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20520-3
Online ISBN: 978-3-540-40004-2
eBook Packages: Springer Book Archive