Abstract
We consider hypergroups associated with Jacobi functions ϕ (αβ)κ (x), (α≥β≥−1/2). We prove the existence of a dual convolution structure on [0,+∞[⋃i(]0,s 0]⋃{ρ{) ρ=α+β+1,s 0=min(ρ,α−β+1). Next we establish a Lévy-Khintchine type formula which permits to characterize the semigroup and the infinitely divisible probabilities associated with this dual convolution, finally we prove a central limit theorem.
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Nejib, B.S. Convolution semigroups and central limit theorem associated with a dual convolution structure. J Theor Probab 7, 417–436 (1994). https://doi.org/10.1007/BF02214276
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DOI: https://doi.org/10.1007/BF02214276