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Classes of measures which can be embedded in the Simple Symmetric Random Walk

Abstract:

We characterize the possible distributions of a stopped simple symmetric random walk Xτ, where τ is a stopping time relative to the natural filtration of (Xn). We prove that any probability measure on ℤ can be achieved as the law of Xτ where τ is a minimal stopping time, but the set of measures obtained under the further assumption that (X n∧τ : n ≥ 0) is a uniformly integrable martingale is a fractal subset of the set of all centered probability measures on ℤ. This is in sharp contrast to th...

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Publication status:
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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Role:
Author
Journal:
ELECTRONIC JOURNAL OF PROBABILITY
Volume:
13
Pages:
1203-1228
Publication date:
2008-07-31
EISSN:
1083-6489
ISSN:
1083-6489
URN:
uuid:44114d8e-9bbc-4841-ba60-020e65ae9639
Source identifiers:
188690
Local pid:
pubs:188690

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