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SUMMARY:Empirical Measure and Small Noise Asymptotics under Large Deviatio
 n Scaling for Interacting Diffusions - Amarjit Budhiraja (UNC Chapel Hill)
DTSTART:20200225T140000Z
DTEND:20200225T150000Z
UID:TALK138100@talks.cam.ac.uk
CONTACT:Perla Sousi
DESCRIPTION:Consider a collection of particles whose state evolution is de
 scribed through a system of interacting diffusions in which each particle\
 nis driven by an independent individual source of noise and also by a smal
 l amount of noise that is common to all particles. The interaction between
  the particles is due to the common noise and also through the drift and d
 iffusion coefficients that depend on the state empirical measure. We study
  large deviation behavior of the empirical measure process which is govern
 ed by two types of scaling\, one corresponding to mean field asymptotics a
 nd the other to the Freidlin-Wentzell small noise asymptotics. \nDifferent
  levels of intensity of the small common noise lead to different types of 
 large deviation behavior\, and we provide a precise characterization of th
 e various regimes. We also study large deviation behavior of  interacting 
 particle systems approximating various types of Feynman-Kac functionals. P
 roofs are based on stochastic control representations for exponential func
 tionals of Brownian motions and on uniqueness results for weak solutions o
 f stochastic differential equations associated with controlled nonlinear M
 arkov processes.
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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