On the area swept by a biased diffusion till its first-exit time: Martingale approach and gambling opportunities
| Autor: | Sarmiento, Yonathan, Das, Debraj, Roldán, Édgar |
|---|---|
| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Indian J Phys (2024) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s12648-024-03182-8 |
| Popis: | Using martingale theory, we compute, in very few lines, exact analytical expressions for various first-exit-time statistics associated with one-dimensional biased diffusion. Examples include the distribution for the first-exit time from an interval, moments for the first-exit site, and functionals of the position, which involve memory and time integration. As a key example, we compute analytically the mean area swept by a biased diffusion until it escapes an interval that may be asymmetric and have arbitrary length. The mean area allows us to derive the hitherto unexplored cross-correlation function between the first-exit time and the first-exit site, which vanishes only for exit problems from symmetric intervals. As a colophon, we explore connections of our results with gambling, showing that betting on the time-integrated value of a losing game it is possible to design a strategy that leads to a net average win. Comment: 14 pages, 5 figures |
| Databáze: | arXiv |
| Externí odkaz: |
|