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SUMMARY:Probabilistic representation for the solutions of generalized frac
 tional equations and generalized operator-valued Mittag-Leffler functions 
 - Vassili Kolokoltsov (University of Warwick)
DTSTART:20220125T093000Z
DTEND:20220125T100000Z
UID:TALK169154@talks.cam.ac.uk
DESCRIPTION:2) Vassili Kolokoltsov\nTitle: Probabilistic representation fo
 r the solutions of generalized fractional equations and generalized operat
 or-valued Mittag-Leffler functions\nAstract: We present a unifying approac
 h to theanalysis of generalized fractional Partial DifferentialEquations o
 f Caputo-Djerbashian and Riemann-Liouville type. This point of view leads 
 to the path integral representation for the solutions of these equations\,
  which is seen to bestable with respect to the initial data and key parame
 ters and is directly amenable to numeric calculations (Monte-Carlo simulat
 ion). In many casesthese solutions can be compactly presented via the wide
  class of operator-valuedanalytic functions of the Mittag-Leffler type\, w
 hich are proved to beexpressed as the Laplace transforms of the exit times
  of monotone Markov processes. &nbsp\;\n&nbsp\;\n&nbsp\;
LOCATION:Seminar Room 2\, Newton Institute
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