Displaying similar documents to “A characterization of harmonic measure and Markov processes whose hitting distributions are preserved by rotations translations and dilatations”

Stochastic harmonic morphisms : functions mapping the paths of one diffusion into the paths of another

Bernt Oksendal, L. Csink (1983)

Annales de l'institut Fourier

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We give several necessary and sufficient conditions that a function φ maps the paths of one diffusion into the paths of another. One of these conditions is that φ is a harmonic morphism between the associated harmonic spaces. Another condition constitutes an extension of a result of P. Lévy about conformal invariance of Brownian motion. The third condition implies that two diffusions with the same hitting distributions differ only by a chance of time scale. We also obtain a converse...

Hitting probabilities and potential theory for the brownian path-valued process

Jean-François Le Gall (1994)

Annales de l'institut Fourier

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We consider the Brownian path-valued process studied in [LG1], [LG2], which is closely related to super Brownian motion. We obtain several potential-theoretic results related to this process. In particular, we give an explicit description of the capacitary distribution of certain subsets of the path space, such as the set of paths that hit a given closed set. These capacitary distributions are characterized as the laws of solutions of certain stochastic differential equations. They solve...