×

Harmonic functions and mass cancellation. (English) Zbl 0391.60065


MSC:

60J05 Discrete-time Markov processes on general state spaces
60J65 Brownian motion
31B05 Harmonic, subharmonic, superharmonic functions in higher dimensions
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] M. A. Akcoglu and R. W. Sharpe, Ergodic theory and boundaries, Trans. Amer. Math. Soc. 132 (1968), 447 – 460. · Zbl 0162.19402
[2] John R. Baxter, Restricted mean values and harmonic functions, Trans. Amer. Math. Soc. 167 (1972), 451 – 463. · Zbl 0238.31006
[3] J. R. Baxter and R. V. Chacon, Potentials of stopped distributions, Illinois J. Math. 18 (1974), 649 – 656. · Zbl 0323.60050
[4] J. R. Baxter and R. V. Chacon, Stopping times for recurrent Markov processes, Illinois J. Math. 20 (1976), no. 3, 467 – 475. · Zbl 0335.60036
[5] R. V. Chacon, Potential processes, Trans. Amer. Math. Soc. 226 (1977), 39 – 58. · Zbl 0366.60106
[6] S. R. Foguel, Iterates of a convolution on a non abelian group, Ann. Inst. H. Poincaré Sect. B (N.S.) 11 (1975), no. 2, 199 – 202 (English, with French summary). · Zbl 0312.60004
[7] David Heath, Functions possessing restricted mean value properties, Proc. Amer. Math. Soc. 41 (1973), 588 – 595. · Zbl 0251.31004
[8] Itrel Monroe, On embedding right continuous martingales in Brownian motion, Ann. Math. Statist. 43 (1972), 1293 – 1311. · Zbl 0267.60050
[9] Steven Orey, An ergodic theorem for Markov chains, Z. Wahrscheinlichkeitstheorie Verw. Gebiete 1 (1962), 174 – 176. · Zbl 0109.36302
[10] Donald Ornstein and Louis Sucheston, An operator theorem on \?\(_{1}\) convergence to zero with applications to Markov kernels, Ann. Math. Statist. 41 (1970), 1631 – 1639. · Zbl 0284.60068
[11] William A. Veech, A zero-one law for a class of random walks and a converse to Gauss’ mean value theorem, Ann. of Math. (2) 97 (1973), 189 – 216. · Zbl 0282.60048
[12] William A. Veech, A converse to the mean value theorem for harmonic functions, Amer. J. Math. 97 (1975), no. 4, 1007 – 1027. · Zbl 0324.31002
[13] -, The core of a measurable set and a problem in potential theory (preprint).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.