Poisson point processes attached to symmetric diffusions
On unique extension of time changed reflecting brownian motions
Let be an unbounded domain in ℝ with ≥3. We show that if contains an unbounded uniform domain, then the symmetric reflecting brownian motion (RBM) on is transient. Next assume that RBM on is transient and let be its time change by Revuz measure ()() d for a strictly positive continuous integrable function on . We further show that if there is some >0 so that ∖̅(̅0̅,̅ ̅) is an unbounded uniform domain, then admits one and only one symmetric diffusion that genuinely...
On semi-martingale characterizations of functionals of symmetric Markov processes.
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