Preprint: (To appear in
Séminaire de Probabilités XXXVII)
The Codimension of the Zeros of a Stable Process
in Random Scenery
D. Khoshnevisan
Abstract.
We show that for any a\in (1,2], the
(stochastic) codimension of the zeros of
an a-stable process in random scenery
is identically 1-(2 a)-1. As an immediate
consequence, we deduce that the Hausdorff dimension
of the zeros of the latter process is almost surely
(2 a)-1. This solves Conjecture 5.2
of Khoshnevisan and Lewis (1999b), thereby refining
a computation of Xiao (1999).
Keywords.
Random walk in random scenery,
stochastic codimension,
Hausdorff dimension.
AMS Classification (2000)
60K37
Support. Research supported in part by grants from
- U.S. National Science Foundation
- North Atlantic Treaty Organization
Pre/E-Prints. This paper is available in
Davar Khoshnevisan
Department of Mathematics
University of Utah
155 S, 1400 E JWB 233
Salt Lake City, UT 84112-0090, U.S.A.
davar@math.utah.edu
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Last Update: October 1, 2001
© 2001 - Davar Khoshnevisan