Journal article
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:
- Published
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Bibliographic Details
- Journal:
- ELECTRONIC JOURNAL OF PROBABILITY
- Volume:
- 13
- Pages:
- 1203-1228
- Publication date:
- 2008-07-31
- EISSN:
-
1083-6489
- ISSN:
-
1083-6489
- Source identifiers:
-
188690
Item Description
- Language:
- English
- Keywords:
- Pubs id:
-
pubs:188690
- UUID:
-
uuid:44114d8e-9bbc-4841-ba60-020e65ae9639
- Local pid:
- pubs:188690
- Deposit date:
- 2012-12-19
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- Copyright date:
- 2008
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