First passage time of Dickman subordinator and non-local operators

Leonenko Nikolai, Cardiff University

The convolution-type fractional derivatives generated by Dickman subordinator and inverse Dickman subordinator are discussed. The series representations of densities of the Dickman subordinator and inverse Dickman subordinator are also obtained, which could be helpful for computational purposes. Moreover, the space and time-fractional Poisson-Dickman processes, space-fractional Skellam Dickman process and non-homogenous Poisson Dickman process are introduced and their main properties are studied. This is joint work with N.Gupta (Indian Statistical Institute, New Delhi, India), A.Kumar(Indian Institute of Technology, Ropar, India) and J.Vaz (Unicamp, Campinas, Brazil).

Area: CS30 - Fractional processes and Malliavin calculus for stochastic models (Enrica Pirozzi)

Keywords: Dickman subordinator, convolution type fractional derivatives, inverse Dickman subordinator, Poisson-Dickman process

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