On the Local Time of Random Walks Associated with Gegenbauer Polynomials

Nadine Guillotin-Plantard ()
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Nadine Guillotin-Plantard: Université de Lyon

Journal of Theoretical Probability, 2011, vol. 24, issue 4, 1157-1169

Abstract: Abstract The local time of random walks associated with Gegenbauer polynomials $P_{n}^{(\alpha)}(x)$ , x∈[−1,1], is studied in the recurrent case: $\alpha\in [-\frac{1}{2},0]$ . When α is nonzero, the limit distribution is given in terms of a Mittag-Leffler distribution. The proof is based on a local limit theorem for the random walk associated with Gegenbauer polynomials. As a by-product, we derive the limit distribution of the local time of some particular birth-and-death Markov chains on ℕ.

Keywords: Random walk; Local time; Local limit theorem; Gegenbauer polynomials; Markov chain; Transition kernel; Recurrence; Transience; Birth and death process; 60J10; 60J55; 60F05; 60B99 (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/s10959-010-0297-4

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