Tutte’s invariant approach for Brownian motion reflected in the quadrant

Author:

Franceschi S.,Raschel Kilian

Abstract

We consider a Brownian motion with negative 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.

Publisher

EDP Sciences

Subject

Statistics and Probability

Reference30 articles.

1. Analysis of Models Reducible to a Class of Diffusion Processes in the Positive Quarter Plane

2. O. Bernardi, M. Bousquet-Mélou and K. Raschel, Counting quadrant walks via Tutte’s invariant method. In 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016) (2016) 203–214.

3. M. Bousquet-Mélou and M. Mishna, Walks with small steps in the quarter plane. In Algorithmic probability and combinatorics. Vol. 520 of Contemp. Math. Amer. Math. Soc. Providence, RI (2010) 1–39.

4. Obliquely reflected Brownian motion in nonsmooth planar domains

5. J. Dai, Steady-state analysis of reflected Brownian motions: Characterization, numerical methods and queueing applications. ProQuest LLC, Ann Arbor, MI. Ph.D. thesis, Stanford University (1990).

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