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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.
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Contributor : Sandro Franceschi Connect in order to contact the contributor
Submitted on : Monday, July 10, 2017 - 12:14:54 PM
Last modification on : Tuesday, January 11, 2022 - 5:56:09 PM
Long-term archiving on: : Friday, January 26, 2018 - 3:31:35 PM


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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⟩



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