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**Harvard**

den Hollander, F., Steif, J. och van der Wal, P. (2005) *Bad configurations for random walk in random scenery and related subshifts*.

** BibTeX **

@article{

den Hollander2005,

author={den Hollander, F. and Steif, Jeffrey and van der Wal, P.},

title={Bad configurations for random walk in random scenery and related subshifts},

journal={Stochastic Processes and their Applications},

issn={03044149 },

volume={115},

issue={7},

pages={1209-1232},

abstract={In this paper we consider an arbitrary irreducible random walk on ℤd, d ≥ 1, with i.i.d. increments, together with an arbitrary i.i.d. random scenery. Walk and scenery are assumed to be independent. Random walk in random scenery (RWRS) is the random process where time is indexed by ℤ, and at each unit of time both the step taken by the walk and the scenery value at the site that is visited are registered. Bad configurations for RWRS are the discontinuity points of the conditional probability distribution for the configuration at the origin of time given the configuration at all other times. We show that the set of bad configurations is non-empty. We give a complete description of this set and compute its probability under the random scenery measure. Depending on the type of random walk, this probability may be zero or positive. For simple symmetric random walk we get three different types of behavior depending on whether d = 1, 2, d = 3, 4 or d ≥ 5. Our classification is actually valid for a class of subshifts having a certain determinative property, which we call specifiable, of which RWRS is an example. We also consider bad configurations w.r.t. a finite time interval (replacing the origin) and obtain an almost complete generalization of our results. Remarkably, this extension turns out to be somewhat delicate.},

year={2005},

}

** RefWorks **

RT Journal Article

SR Electronic

ID 111004

A1 den Hollander, F.

A1 Steif, Jeffrey

A1 van der Wal, P.

T1 Bad configurations for random walk in random scenery and related subshifts

YR 2005

JF Stochastic Processes and their Applications

SN 03044149

VO 115

IS 7

SP 1209

OP 1232

AB In this paper we consider an arbitrary irreducible random walk on ℤd, d ≥ 1, with i.i.d. increments, together with an arbitrary i.i.d. random scenery. Walk and scenery are assumed to be independent. Random walk in random scenery (RWRS) is the random process where time is indexed by ℤ, and at each unit of time both the step taken by the walk and the scenery value at the site that is visited are registered. Bad configurations for RWRS are the discontinuity points of the conditional probability distribution for the configuration at the origin of time given the configuration at all other times. We show that the set of bad configurations is non-empty. We give a complete description of this set and compute its probability under the random scenery measure. Depending on the type of random walk, this probability may be zero or positive. For simple symmetric random walk we get three different types of behavior depending on whether d = 1, 2, d = 3, 4 or d ≥ 5. Our classification is actually valid for a class of subshifts having a certain determinative property, which we call specifiable, of which RWRS is an example. We also consider bad configurations w.r.t. a finite time interval (replacing the origin) and obtain an almost complete generalization of our results. Remarkably, this extension turns out to be somewhat delicate.

LA eng

DO 10.1016/j.spa.2005.03.001

LK http://dx.doi.org/10.1016/j.spa.2005.03.001

OL 30