Article ; Online: Leftward, rightward, and complete exit-time distributions of jump processes.
2023 Volume 107, Issue 5-1, Page(s) 54109
Abstract: First-passage properties of continuous stochastic processes confined in a one-dimensional interval are well described. However, for jump processes (discrete random walks), the characterization of the corresponding observables remains elusive, despite ... ...
| Abstract | First-passage properties of continuous stochastic processes confined in a one-dimensional interval are well described. However, for jump processes (discrete random walks), the characterization of the corresponding observables remains elusive, despite their relevance in various contexts. Here we derive exact asymptotic expressions for the leftward, rightward, and complete exit-time distributions from the interval [0,x] for symmetric jump processes starting from x_{0}=0, in the large x and large time limit. We show that both the leftward probability F_{[under 0]̲,x}(n) to exit through 0 at step n and rightward probability F_{0,[under x]̲}(n) to exit through x at step n exhibit a universal behavior dictated by the large-distance decay of the jump distribution parametrized by the Levy exponent μ. In particular, we exhaustively describe the n≪(x/a_{μ})^{μ} and n≫(x/a_{μ})^{μ} limits and obtain explicit results in both regimes. Our results finally provide exact asymptotics for exit-time distributions of jump processes in regimes where continuous limits do not apply. |
|---|---|
| MeSH term(s) | Stochastic Processes ; Probability ; Time Factors |
| Language | English |
| Publishing date | 2023-06-17 |
| Publishing country | United States |
| Document type | Journal Article |
| ZDB-ID | 2844562-4 |
| ISSN | 2470-0053 ; 2470-0045 |
| ISSN (online) | 2470-0053 |
| ISSN | 2470-0045 |
| DOI | 10.1103/PhysRevE.107.054109 |
| Database | MEDical Literature Analysis and Retrieval System OnLINE |
More links
Kategorien
Order via subito
This service is chargeable due to the Delivery terms set by subito. Orders including an article and supplementary material will be classified as separate orders. In these cases, fees will be demanded for each order.