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SUMMARY:Random Periodicity: Theory and Modelling
DTSTART;VALUE=DATE-TIME:20190124T153000Z
DTEND;VALUE=DATE-TIME:20190124T163000Z
DTSTAMP;VALUE=DATE-TIME:20191022T110348Z
UID:indico-event-4269@indico.math.cnrs.fr
DESCRIPTION:Random periodicity is ubiquitous in the real world. In this ta
lk\, I will provide the concepts of random periodic paths and periodic mea
sure to mathematically describe random periodicity. These two different no
tions are “equivalent”. An ergodic theory is established. For Markovia
n random dynamical systems\, in the random periodic case\, the infinitesim
al generator of the Markovian has infinite number of equally placed simple
eigenvalues including 0 on the imaginary axis\, in contrast to the mixing
stationary case in which the Koopman-von Neumann Theorem says there is on
ly one simple eigenvalue 0 on the imaginary axis. Examples of of Markov
chains\, random mappings\, stochastic differential equations and stochasti
c partial differential equations with random periodic paths or periodic me
asures will be provided. This theory implies law of large numbers\, centra
l limit theorems and applications to time series (touched if time permits)
.\n\nhttps://indico.math.cnrs.fr/event/4269/
LOCATION:Institut de Mathématiques de Bourgogne René Baire
URL:https://indico.math.cnrs.fr/event/4269/
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