Large deviation of some infinite-dimensional Markov processes. (English) Zbl 0637.60036

This paper considers the Ornstein-Uhlenbeck process on the function space C[0,1], which here is the continuous real-valued functions on [0,1] with value 0 at 0. This process is a Markov process with transition probabilities \(p_ t(x,dy)\) given by \(P(e^{-t/2} x+(1-e^{- t})^{1/2} B(\cdot)\in dy)\) where B is a standard Brownian motion.
A large deviation principle of the kind discussed in M. D. Donsker and S. R. S. Varadhan, Commun. Pure Appl. Math. 36, 183-212 (1983; Zbl 0512.60068) is established for this process. Donsker and Varadhan gave the corresponding result for the finite-dimensional process as an application of their general theorem, but their conditions do not hold for the process described above and other arguments are therefore used.
Reviewer: J.D.Biggins


60F10 Large deviations
60J25 Continuous-time Markov processes on general state spaces


Zbl 0512.60068
Full Text: DOI


[1] DOI: 10.1214/aop/1176993068 · Zbl 0559.60031 · doi:10.1214/aop/1176993068
[2] DOI: 10.1002/cpa.3160360204 · Zbl 0512.60068 · doi:10.1002/cpa.3160360204
[3] Hida T., Stationary Stochastic Processes (1970) · Zbl 0214.16401
[4] DOI: 10.1007/BFb0088721 · doi:10.1007/BFb0088721
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