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CATEGORIES:Probability
SUMMARY:Empirical Measure and Small Noise Asymptotics unde
r Large Deviation Scaling for Interacting Diffusio
ns - Amarjit Budhiraja (UNC Chapel Hill)
DTSTART;TZID=Europe/London:20200225T140000
DTEND;TZID=Europe/London:20200225T150000
UID:TALK138100AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/138100
DESCRIPTION:Consider a collection of particles whose state evo
lution is described through a system of interactin
g diffusions in which each particle\nis driven by
an independent individual source of noise and also
by a small amount of noise that is common to all
particles. The interaction between the particles i
s due to the common noise and also through the dri
ft and diffusion coefficients that depend on the s
tate empirical measure. We study large deviation b
ehavior of the empirical measure process which is
governed by two types of scaling\, one correspondi
ng to mean field asymptotics and the other to the
Freidlin-Wentzell small noise asymptotics. \nDiffe
rent levels of intensity of the small common noise
lead to different types of large deviation behavi
or\, and we provide a precise characterization of
the various regimes. We also study large deviation
behavior of interacting particle systems approxi
mating various types of Feynman-Kac functionals. P
roofs are based on stochastic control representati
ons for exponential functionals of Brownian motion
s and on uniqueness results for weak solutions of
stochastic differential equations associated with
controlled nonlinear Markov processes.
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0W
B
CONTACT:Perla Sousi
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