Supremum distribution of Bessel process of drifting Brownian motion
Andrzej Py\'c, Grzegorz Serafin, Tomasz \.Zak
TL;DR
This paper derives the distribution of the supremum of the distance process of a three-dimensional drifting Brownian motion, providing an explicit series formula and elementary bounds for its density.
Contribution
It introduces an explicit infinite-series formula for the supremum distribution of a drifting Brownian motion's distance process.
Findings
Provides an infinite-series formula for the supremum density.
Offers elementary function estimates for the distribution.
Applies to diffusion processes with drift in three dimensions.
Abstract
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsStochastic processes and financial applications · Stochastic processes and statistical mechanics · Random Matrices and Applications