Exit time, Green function and semilinear elliptic equations.
Girsanov and Feynman–Kac type transformations for symmetric Markov processes
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...
Uniqueness for reflecting brownian motion in lip domains
Heat kernel estimates for the Dirichlet fractional Laplacian
We consider the fractional Laplacian on an open subset in with zero exterior condition. We establish sharp two-sided estimates for the heat kernel of such a Dirichlet fractional Laplacian in open sets. This heat kernel is also the transition density of a rotationally symmetric -stable process killed upon leaving a open set. Our results are the first sharp twosided estimates for the Dirichlet heat kernel of a non-local operator on open sets.
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