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

@article{Franceschi2017TuttesIA,
  title={Tutte's invariant approach for Brownian motion reflected in the quadrant},
  author={S. Franceschi and K. Raschel},
  journal={Esaim: Probability and Statistics},
  year={2017},
  volume={21},
  pages={220-234}
}
  • S. Franceschi, K. Raschel
  • Published 2017
  • Mathematics
  • Esaim: Probability and Statistics
  • 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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