This chapter is devoted to the study of additive functionals of symmetric Markov processes under the same setting as in the preceding chapter, namely, that E is a locally compact separable metric space, B(E) is the family of all Borel sets of E, and m is a positive Radon measure on E with supp[m] = E, and this chapter considers an m-symmetric Hunt process X = (Ω,M,Xₜ,ζ,Pₓ) on (E,B(E)) whose Dirichlet form (E,F) on L²(E; m) is regular on L²(E; m). The transition function and the resolvent of X are denoted by {Pₜ; t ≥ 0}, {R
α, α > 0}, respectively. B*(E) will denote the family of all universally measurable subsets of E. Any numerical function f defined on E will be always extended to E
∂ by setting f(∂) = 0.
Large deviation for additive functionals of symmetric Markov processes
