BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//wp-events-plugin.com//7.2.3.1//EN
BEGIN:VEVENT
UID:572@lincs.fr
DTSTART;TZID=Europe/Paris:20201208T140000
DTEND;TZID=Europe/Paris:20201208T170000
DTSTAMP:20201208T071905Z
URL:https://www.lincs.fr/events/thesis-defense-speed-of-convergence-of-dif
 fusion-approximations/
SUMMARY:Thesis defense "Speed of convergence of diffusion approximations"
DESCRIPTION:In many fields of interest\, Markov processes are a primary
 modelisation tool for random processes. Unfortunately it is often necessary
 to use very large or even infinite dimension state spaces\, making the
 exact analysis of the various characteristics of interest (stability\,
 stationary law\, hitting times of certain domains\, etc.) of the process
 difficult or even impossible . For quite a time\, thanks in particular to
 martingale theory\, it has been possible to make use of approximations by
 brownian diffusions. This enables an approximate analysis of the initial
 problem.\nThe main drawback of this approach is that it does not measure
 the error made in this approximation. The purpose is to dévelop a theory
 of error calculation for diffusion approximations .\nFor some time\, the
 developement of the Stein-Malliavin method has enabled to get some
 precision over speed of convergence in classical theorems such as the
 Donsker theorem (functionnal convergence&nbsp\; of a random walk towards
 the Brownian motion)&nbsp\; or in the generalisation of the Binomial
 Poisson approximation path by path.\nIn this work we intend to extend the
 development of this theory for Markovian processes such as those than can
 be found in queueing theory\, in epidemiology or in other fields of
 application.\nStarting from the representation of Markov processes as
 Poisson measures\, we extend the method developped by Laurent Decreusefond
 and Laure Coutin to assess the speed of convergence in diffusion
 approximations . To do so\, we extend the Stein-Malliavin method to vectors
 of&nbsp\; processes rather than a single process. The limit is a gaussian
 process changed in time. The Stein Malliavin method being mainly developped
 to calculate&nbsp\; convergence towards the standard Brownian motion\, it
 is adapted to the problem of convergence towards a time changend process
 using linear approximation methods. We therefore make use of Gaussian
 analysis to assess the dependency between the various time periods and to
 functionnal analysis to elect the right probabilistic spaces.\nHere's the
 streaming
 link:\nhttps://telecom-paris.zoom.us/j/93338351493?pwd=YjFRYStvVUR3YlBYWVJ1
 anBHYmNiQT09\n&nbsp\;\nID de réunion&nbsp\;: 933 3835 1493\nCode
 secret&nbsp\;: 226860
CATEGORIES:PhD Defense
END:VEVENT
BEGIN:VTIMEZONE
TZID:Europe/Paris
X-LIC-LOCATION:Europe/Paris
BEGIN:STANDARD
DTSTART:20201025T020000
TZOFFSETFROM:+0200
TZOFFSETTO:+0100
TZNAME:CET
END:STANDARD
END:VTIMEZONE
END:VCALENDAR