On the equation μ t + s = μ s ∗ T s μ t

Abstract

We prove that any solution of the equation μt+s = μs∗Tsμt consists of infinitely divisible measures, and that there are constants (bt)t≥0 so that t 7→ μt∗δ−bt is continuous. AMS classification: 47D07; 60H10 

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