Renewal Theorems for Singular Differential Operators

Léonard Gallardo () and Khalifa Trimèche
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Léonard Gallardo: Université de Tours
Khalifa Trimèche: Faculté des Sciences de Tunis

Journal of Theoretical Probability, 2002, vol. 15, issue 1, 161-205

Abstract: Abstract Let * be the convolution on M( $${\mathbb{R}}$$ +) associated with a second order singular differential operator L on ]0, +∞[. If μ is a probability measure on $${\mathbb{R}}$$ + with suitable moment conditions, we study how to normalize the measures μ* n ; n∈ $${\mathbb{N}}$$ } (resp. $$\left\{ {\varepsilon _x * \sum _{n\; = \;0}^\infty \mu ^{ * n} } \right\}$$ ) in order to get vague convergence if n→+∞ (resp. x→+∞). The results depend on the asymptotic drift of the operator L and on a precise study of the asymptotic behaviour of its eigenfunctions.

Keywords: renewal theorems; Laplace operator; potential measure; eigenfunctions; vague convergence (search for similar items in EconPapers)
Date: 2002
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DOI: 10.1023/A:1013895502747

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