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Occupation time limit theorems for independent random walks
| Content Provider | Semantic Scholar |
|---|---|
| Author | Lee, Tzong-Yow Rémillard, Bruno |
| Copyright Year | 1994 |
| Abstract | We summarize many limit theorems for systems of independent simple random walks in Z. These theorems are classiied into four classes: weak convergence, moderate deviations, large deviations and enormous deviations. A hierarchy of relations is pointed out and some open problems are posed. Extensions to function spaces are also mentioned. 1. Introduction In this paper we review many results on the asymptotic behavior of func-tionals of the occupation time for systems of independent random walks. Some extensions to general Markov processes are also mentioned and given references. We do not intend to detail the corresponding literature for the branching models, neither for the interacting models; we refer the reader to CG85b, Lee93b, IL93] for the branching models, and to CG83, BCG88, Cox88, Lan92], for the interacting models. A quick look at the few results obtained so far for the branching and the interacting models reveals that qualitatively, the same results as in the case of independent random walks turn out to be true. For results obtained before 1985, we refer the reader to CG85a] for a nice review. Of course, results for the branching and interacting models are more diicult to prove, but the results presented in this paper will however tell us what results to anticipate in these models. By posing corresponding problems for branching and interacting models, one has many conjectures to verify. We believe that this direction of research will be challenging and fruitful, and hope that our summary could arouse some interests for these topics. |
| Starting Page | 151 |
| Ending Page | 163 |
| Page Count | 13 |
| File Format | PDF HTM / HTML |
| DOI | 10.1090/crmp/005/12 |
| Alternate Webpage(s) | http://helios.uqtr.uquebec.ca/~remillar/tyl3.ps |
| Alternate Webpage(s) | https://doi.org/10.1090/crmp%2F005%2F12 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
