BEGIN:VCALENDAR VERSION:2.0 PRODID:-//Talks.cam//talks.cam.ac.uk// X-WR-CALNAME:Talks.cam BEGIN:VEVENT SUMMARY:Dickman-type stochastic processes and non-local operators - Nikola i Leonenko (Cardiff University) DTSTART:20240918T140000Z DTEND:20240918T150000Z UID:TALK220612@talks.cam.ac.uk DESCRIPTION:The Dickman function\, originally appeared in Ramanujan&rsquo\ ;s unpublished notes and first explored by Karl Dickman in the field of nu mber theory\, has garnered interesting recognition in recent years. This f unction has given rise to the Dickman distribution [1\,2] and\, subsequent ly\, the Dickman subordinator [3]. The Dickman distribution also appears i n various limiting schemes [1]. It also appears as a special case of Verva at perpetuities.\nWe introduce the stationary solution of the Ornstein-Uhl enbeck SDE driven by Poisson backward driving Levy process follows a Dickm an marginal distribution [2]. Additionally we investigate superpositions o f such processes which has a long-range dependent properties and marginal Dichman distribution\, limit theorems for such a processes and intermitten cy in the spirit of the papers [4\,5\,6\,7]. The distribution of the first passage time process for Dickman subordinator is discussed  \;as well as the corresponding convolution type non-local operator (or Dickman frac tional derivatives)[2]. The nonlocal Poisson processes are introduced as t ime-change Poisson process and independent inverse Dichman subordinator in the spirit of fractional Poisson process obtained  \;as time-change P oisson process and independent inverse stable subordinator[8\,9].\nThe fir st part is joint work with D. Grahovac (Osijek University\, Croatia)\, A.K ovtun and A.Pepelyshev (Cardiff University\, UK).\nThe second part is base d on the 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). LOCATION:Seminar Room 1\, Newton Institute END:VEVENT END:VCALENDAR