Tutte's invariant approach for Brownian motion reflected in the quadrant
Probability
2019-11-07 v2
Abstract
We consider a Brownian motion with drift in the quarter plane with orthogonal reflection on the axes. The Laplace transform of its stationary distribution satisfies a functional equation, which is reminiscent from equations arising in the enumeration of (discrete) quadrant walks. We develop a Tutte's invariant approach to this continuous setting, and we obtain an explicit formula for the Laplace transform in terms of generalized Chebyshev polynomials.
Keywords
Cite
@article{arxiv.1602.03054,
title = {Tutte's invariant approach for Brownian motion reflected in the quadrant},
author = {Sandro Franceschi and Kilian Raschel},
journal= {arXiv preprint arXiv:1602.03054},
year = {2019}
}
Comments
14 pages, 3 figures