Analytic approach for reflected Brownian motion in the quadrant

Abstract : Random walks in the quarter plane are an important object both of combinatorics and probability theory. Of particular interest for their study, there is an analytic approach initiated by Fayolle, Iasnogorodski and Malyšev , and further developed by the last two authors of this note. The outcomes of this method are explicit expressions for the generating functions of interest, asymptotic analysis of their coefficients, etc. Although there is an important literature on reflected Brownian motion in the quarter plane (the continuous counterpart of quadrant random walks), an analogue of the analytic approach has not been fully developed to that context. The aim of this note is twofold: it is first an extended abstract of two recent articles of the authors of this paper, which propose such an approach; we further compare various aspects of the discrete and continuous analytic approaches.
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Communication dans un congrès
International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms, Jul 2016, Cracovie, Poland. Proceedings of the 27th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms, Krakow, Poland, 4-8 July 2016. 〈http://www.aofa.tcs.uj.edu.pl/accepted-papers.html〉
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  • HAL Id : hal-01317611, version 1
  • ARXIV : 1605.03057

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Sandro Franceschi, Irina Kurkova, Kilian Raschel. Analytic approach for reflected Brownian motion in the quadrant. International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms, Jul 2016, Cracovie, Poland. Proceedings of the 27th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms, Krakow, Poland, 4-8 July 2016. 〈http://www.aofa.tcs.uj.edu.pl/accepted-papers.html〉. 〈hal-01317611〉

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