Displaying similar documents to “Dirichlet forms, quasiregular functions and Brownian motion.”

Uniqueness of Brownian motion on Sierpiński carpets

Martin Barlow, Richard F. Bass, Takashi Kumagai, Alexander Teplyaev (2010)

Journal of the European Mathematical Society

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We prove that, up to scalar multiples, there exists only one local regular Dirichlet form on a generalized Sierpi´nski carpet that is invariant with respect to the local symmetries of the carpet. Consequently, for each such fractal the law of Brownian motion is uniquely determined and the Laplacian is well defined.

On unique extension of time changed reflecting brownian motions

Zhen-Qing Chen, Masatoshi Fukushima (2009)

Annales de l'I.H.P. Probabilités et statistiques

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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...