Selective Limit Theorems for Random Walks on Parabolic Biangle and Triangle Hypergroups

Maher Mili
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Maher Mili: Faculty of Sciences of Monastir

Journal of Theoretical Probability, 2000, vol. 13, issue 3, 717-731

Abstract: Abstract Let K be respectively the parabolic biangle and the triangle in $${\mathbb{R}}^2$$ and $$\left( {\alpha \left( p \right)} \right)_{p \in {\mathbb{N}}} $$ be a sequence in [0, +∞[ such that limp→∞ α(p)=+∞. According to Koornwinder and Schwartz,(7) for each $$p \in {\mathbb{N}}$$ there exist a convolution structure (*α(p)) such that (K, *α(p)) is a commutative hypergroup. Consider now a random walk $$\left( {X_j^{{\alpha }\left( p \right)} } \right)_{j \in {\mathbb{N}}}$$ on (K, *α(p)), assume that this random walk is stopped after j(p) steps. Then under certain conditions given below we prove that the random variables $$\left( {X_j^{{\alpha }\left( p \right)} } \right)_{p \in {\mathbb{N}}}$$ on K admit a selective limit theorems. The proofs depend on limit relations between the characters of these hypergroups and Laguerre polynomials that we give in this work.

Keywords: random walks; hypergroups; Laguerre polynomials (search for similar items in EconPapers)
Date: 2000
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DOI: 10.1023/A:1007858411844

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