ISSN:
1432-2064
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Summary Consider a process {Y(t)} of the form $$Y(t) = \sum\limits_1^d {\mathop \smallint \limits_0^t Y_k (X(s)) \circ d\beta _\kappa (s) + \mathop \smallint \limits_0^t Y_0 (X(s))ds} $$ where {X (t)} is a diffusion process on a compact manifold and {βk(t)}, k=1, ..., d, are independent Wiener processes. We derive a Schilder type large deviation principle for the two families: $$\left\{ {\frac{1}{T} \cdot \sum\limits_0^{N - 1} {(Y(k + t) - Y(k))} , t \in [0,1]} \right\}N = 1,2,3...$$ and $$\left\{ {\frac{1}{T} \cdot Y(T \cdot t), t \in [0,1]} \right\}{\text{ }}T \geqq 0$$ as N→∞, respectively T→∞, and identify the corresponding rate functions on C([0, 1]; ℝ). We give a few applications to the asymptotic distribution of the Liapunov exponent of a homogeneous system.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00333151
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