9. The Large Deviation Problem for Empirical Distributions of Markov Processes
Srinivasa R. S. Varadhan · Society for Industrial and Applied Mathematics eBooks · 1984
Let Ω be a space of functions ω(⋅) on −∞<t<∞ with values in a Polish space X. We assume Ω consists of functions with discontinuities only of the first kind, normalized to be right continuous, and with convergence induced by the Skorokhod topology on bounded intervals. In this case Ω is itself a Polish space. Denote by Ωt+ the corresponding space of functions on [t, ∞) with values in X. We denote by ℱts the σ-field in Ω generated by ω(σ) for s≦σ≦t . We denote the translation map on Ω by θt , i.e., (θtω)(s)=ω(s+t) .