Abstract : In this paper we study the Large Deviations Principle (LDP in abbreviation) for a class of
Stochastic Partial Differential Equations (SPDEs) in the whole space Rd, with arbitrary
dimension d ≥ 1, under random influence which is a Gaussian noise, white in time and
correlated in space. The differential operator is a fractional derivative operator. We prove
a Large deviations principle for our equation, using a weak convergence approach based
on a variational representation of functionals of infinite-dimensional Brownian motion.
This approach reduces the proof of LDP to establishing basic qualitative properties for
controlled analogues of the original stochastic system.