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A characterization of harmonic measure and Markov processes whose hitting distributions are preserved by rotations translations and dilatations

Bernt Oksendal, Daniel W. Stroock (1982)

Annales de l'institut Fourier

The exit distribution for open sets of a path-continuous, strong Markov process in R n is characterized as a weak star limit of successive spherical sweepings of measures, starting with the unit point mass. Then this is used to prove that two path-continuous strong Markov processes with identical exit distributions from balls when starting form the center, have identical exit distributions from all opens sets, provided they both exit a.s. from bounded sets. This implies that the only path-continuous,...

A family of L 2-spaces associated to the jumps of a Markov process

Valentin Grecea (2011)

Open Mathematics

Given the (canonical) Markov process associated with a sufficiently general semigroup (P t), we establish a result concerning the uniform completeness of a family of L 2-spaces naturally associated with the jumps of the process. An application of this result is presented.

A logarithmic Sobolev form of the Li-Yau parabolic inequality.

Dominique Bakry, Michel Ledoux (2006)

Revista Matemática Iberoamericana

We present a finite dimensional version of the logarithmic Sobolev inequality for heat kernel measures of non-negatively curved diffusion operators that contains and improves upon the Li-Yau parabolic inequality. This new inequality is of interest already in Euclidean space for the standard Gaussian measure. The result may also be seen as an extended version of the semigroup commutation properties under curvature conditions. It may be applied to reach optimal Euclidean logarithmic Sobolev inequalities...

A note on the density of the parabolic area integral.

Ileana Iribarren (2001)

Collectanea Mathematica

The density of the area integral for parabolic functions is defined in analogy with the case of harmonic functions. We prove its equivalence with the local time of the associated martingale. Using probabilistic methods, we show its equivalence in L p -norm with the parabolic area function for p>1.

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