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A function space large deviation principle for certain stochastic integrals. (English) Zbl 0682.60018
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.
Reviewer: L.Arnold

##### MSC:
 60F10 Large deviations 60H05 Stochastic integrals
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##### References:
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