Stochastic applications of Caputo-type convolution operators with\n non-singular kernels

2021/06/30 by Luisa Beghin, Beghin, Luisa, Michèle Caputo +1
Economics, Econometrics and Finance · Mathematics · #26A33 #33B20 #47G20 #60G51 #Advanced Harmonic Analysis Research #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2106.15972

openalex publication_date 2021/06/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider here convolution operators, in the Caputo sense, with\nnon-singular kernels. We prove that the solutions to some integro-differential\nequations with such operators (acting on the space variable) coincide with the\ntransition densities of a particular class of L 'evy subordinators (i.e.\ncompound Poisson processes with non-negative jumps). We then extend these\nresults to the case where the kernels of the operators have random parameters,\nwith given distribution. This assumption allows greater flexibility in the\nchoice of the kernel's parameters and, consequently, of the jumps' density\nfunction.\n

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