A function space large deviation principle for certain stochastic integrals
Let X(t) be a diffusion process on a compact manifold and \[ Y(t)=\int^{t}_{0}Y_ 0(X(s))ds+\sum^{d}_{k=1}\int^{t}_{0}Y_ k(X(s))\circ d\beta_ k(s), \] where \(\beta_ k(\cdot)\), \(1\leq k\leq d\), are independent Wiener processes. The authors prove large deviations principles for \[ \{N^{- 1}\sum^{N-1}_{k=0}(Y(k+t)-Y(k)),\quad 0\leq t\leq 1\}_{N=1,2,3,...}\quad and\quad for\quad \{T^{-1}Y(tT),\quad 0\leq t\leq 1\}_{T\geq 0} \] and identify the corresponding rate functions on C([0,1],\({\mathbb{R}})\). An application to the asymptotics of the Lyapunov exponent of a homogeneous system is given.
scientific article; zbMATH DE number 4117549