×

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

MSC:

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

Citations:

Zbl 0512.60068
PDFBibTeX XMLCite
Full Text: DOI

References:

[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.