Probability Seminar
Thursday, April 14, 2016, 4:30pm, TBD
Ruoyu Wu (UNC-Chapel Hill)
Moderate Deviation Principles for Weakly Interacting Particle Systems
Abstract:- Moderate deviation principles for empirical measure processes
associated with weakly interacting Markov processes are established.
Two families of models are considered: the first corresponds to a
system of interacting diffusions whereas the second describes a
collection of pure jump Markov processes with a countable state space.
For both cases the moderate deviation principle is formulated in terms
of a large deviation principle (LDP), with an appropriate speed
function, for suitably centered and normalized empirical measure
processes. For the first family of models the LDP is established in
the path space of an appropriate Schwartz distribution space whereas
for the second family the LDP is proved in the space of
(the Hilbert space of square summable sequences)-valued paths. Proofs
rely on certain variational representations for exponential
functionals of Brownian motions and Poisson random measures. This is
joint work with Amarjit Budhiraja.
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