A. Bovier, V. Gayrard
Sample path large deviations for a class of Markov chains related to
disordered mean field models
(278K, PS)
ABSTRACT. We prove a large deviation principle
on path space for a class of discrete time Markov processes
whose state space is the intersection of a regular domain $\L\subset \R^d$
with some lattice of spacing $\e$. Transitions from $x$ to $y$ are allowed if
$\e^{-1}(x-y)\in \D$ for some fixed set of vectors $\D$.
The transition
probabilities $p_\e(t,x,y)$, which themselves depend on $\e$,
are allowed to depend on the starting
point $x$ and the time $t$ in a sufficiently regular way,
except near the boundaries, where some singular behaviour
is allowed. The rate function is
identified as an action functional which is given as the integral of
a Lagrange function.
Markov processes of this type arise in the study of mean field dynamics
of disordered mean field models.