On the local time of random walks associated with Gegenbauer polynomials

Details On the local time of random walks associated with Gegenbauer polynomials On the local time of random walks associated with Gegenbauer polynomials

2010-05-25

arxiv.org/abs/1005.4659v1

Mathematics

Probability

12 pages

Scientific paper

The local time of random walks associated with Gegenbauer polynomials $P_n^{(\alpha)}(x),\ x\in [-1,1]$ is studied in the recurrent case: $\alpha\in\ [-\frac{1}{2},0]$. When $\alpha$ 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 $\bbN$.

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