Skip to Main content Skip to Navigation
Journal articles

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

Abstract : We consider a Brownian motion with drift in the quarter plane with orthogonal reflection on the axes. The Laplace transform of its asymptotic 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.
Complete list of metadatas

https://hal.archives-ouvertes.fr/hal-01271870
Contributor : Sandro Franceschi <>
Submitted on : Monday, July 10, 2017 - 12:14:54 PM
Last modification on : Friday, March 27, 2020 - 3:07:28 AM
Document(s) archivé(s) le : Friday, January 26, 2018 - 3:31:35 PM

Files

BVPversionreviseeFrRa.pdf
Files produced by the author(s)

Identifiers

Citation

Sandro Franceschi, Kilian Raschel. Tutte's invariant approach for Brownian motion reflected in the quadrant. ESAIM: Probability and Statistics, EDP Sciences, 2017, ESAIM: PS Volume 21, 2017, 21, pp.220-234. ⟨10.1051/ps/2017006⟩. ⟨hal-01271870v3⟩

Share

Metrics

Record views

281

Files downloads

1098