Supremum distribution of Bessel process of drifting Brownian motion
| Autor: | Pyć, Andrzej, Serafin, Grzegorz, Żak, Tomasz |
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| Rok vydání: | 2015 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Let (B^{(1)}_t ;B^{(2)}_t ;B^{(3)}_t + \mu t) be a three-dimensional Brownian motion with drift \mu, starting at the origin. Then X_t = ||(B^{(1)}_t ;B^{(2)}_t ;B^{(3)}_t +\mu t)||, its distance from the starting point, is a diffusion with many applications. We investigate the distribution of the supremum of (X_t), give an infinite-series formula for its density and an exact estimate by elementary functions. |
| Databáze: | arXiv |
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