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Limit theorems for some continuous-time random walks
| Content Provider | Scilit |
|---|---|
| Author | Jara, M. Komorowski, T. |
| Copyright Year | 2011 |
| Description | In this paper we consider the scaled limit of a continuous-time random walk (CTRW) based on a Markov chain {X n , n ≥ 0} and two observables, τ(∙) and V(∙), corresponding to the renewal times and jump sizes. Assuming that these observables belong to the domains of attraction of some stable laws, we give sufficient conditions on the chain that guarantee the existence of the scaled limits for CTRWs. An application of the results to a process that arises in quantum transport theory is provided. The results obtained in this paper generalize earlier results contained in Becker-Kern, Meerschaert and Scheffler (2004) and Meerschaert and Scheffler (2008), and the recent results of Henry and Straka (2011) and Jurlewicz, Kern, Meerschaert and Scheffler (2010), where {X n , n ≥ 0} is a sequence of independent and identically distributed random variables. |
| Related Links | https://www.cambridge.org/core/services/aop-cambridge-core/content/view/50C7AC9E712B227ADC79EFFB24564E01/S0001867800005140a.pdf/div-class-title-limit-theorems-for-some-continuous-time-random-walks-div.pdf |
| Ending Page | 813 |
| Page Count | 32 |
| Starting Page | 782 |
| ISSN | 00018678 |
| e-ISSN | 14756064 |
| DOI | 10.1017/s0001867800005140 |
| Journal | Advances in Applied Probability |
| Issue Number | 03 |
| Volume Number | 43 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 2011-09-01 |
| Access Restriction | Open |
| Subject Keyword | Advances in Applied Probability Applied Mathematics Mathematical Physics time Random Walk |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics Statistics and Probability |
