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Symmetric Markov Processes, Time Change, and Boundary Theory (LMS-35) by Zhenqing Chen, Masatoshi Fukushima

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ζ(w) < ∞. We can define a σ-finite measure non W so that

image

for 0 < t1 < t2 < · · · < tn and f1, f2,..., fn ∈ B+(E0). Put W+ = {wW : ζ(w) < ∞, wζ− = a}, W = W \ W+ and denote by n+, n the restrictions of nto W+, W, respectively. Owing to the assumptions (A.3), (A.4), it can be shown that

image

from which it follows that n(W) < ∞.

Let p= {pt, t ≥ 0} be the Poisson point process taking values in W with characteristic measure n on an appropriate probability space (Ω, P). Clearly, pis a sum of independent Poisson point processes p+ and p with characteristic ...

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