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On Range and Local Time of Many-dimensional Submartingales
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| Author(s): |
Total Authors: 2
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| Affiliation: | [1] Univ Durham, Dept Math Sci, Durham DH1 3LE - England
[2] Univ Estadual Campinas, Inst Math Stat & Sci Computat, Dept Stat, BR-13083859 Campinas, SP - Brazil
Total Affiliations: 2
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| Document type: | Journal article |
| Source: | JOURNAL OF THEORETICAL PROBABILITY; v. 27, n. 2, p. 601-617, JUN 2014. |
| Web of Science Citations: | 3 |
| Abstract | |
We consider a discrete-time process adapted to some filtration which lives on a (typically countable) subset of a{''}e (d) , da parts per thousand yen2. For this process, we assume that it has uniformly bounded jumps, and is uniformly elliptic (can advance by at least some fixed amount with respect to any direction, with uniformly positive probability). Also, we assume that the projection of this process on some fixed vector is a submartingale, and that a stronger additional condition on the direction of the drift holds (this condition does not exclude that the drift could be equal to 0 or be arbitrarily small). The main result is that with very high probability the number of visits to any fixed site by time n is less than for some delta > 0. This in its turn implies that the number of different sites visited by the process by time n should be at least n(1/2+delta). (AU) | |
| FAPESP's process: | 09/52379-8 - Stochastic modeling of interacting systems |
| Grantee: | Fabio Prates Machado |
| Support type: | Research Projects - Thematic Grants |
| FAPESP's process: | 11/07000-0 - Random walks and related topics |
| Grantee: | Serguei Popov |
| Support type: | Research Grants - Visiting Researcher Grant - International |