×

zbMATH — the first resource for mathematics

Minimal excessive measures and functions. (English) Zbl 0422.60057

MSC:
60J50 Boundary theory for Markov processes
60J45 Probabilistic potential theory
28D05 Measure-preserving transformations
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] J. L. Doob, Stochastic processes, John Wiley & Sons, Inc., New York; Chapman & Hall, Limited, London, 1953. · Zbl 0053.26802
[2] J. L. Doob, Discrete potential theory and boundaries, J. Math. Mech. 8 (1959), 433 – 458; erratum 993. · Zbl 0101.11503
[3] E. B. Dynkin, The exit space of a Markov process, Uspehi Mat. Nauk 24 (1969), no. 4 (148), 89 – 152 (Russian). · Zbl 0201.19801
[4] E. B. Dynkin, Excessive measures and laws of entry for a Markov process, Mat. Sb. (N.S.) 84 (126) (1971), 218 – 253 (Russian). · Zbl 0328.60041
[5] E. B. Dynkin, Initial and final behavior of the trajectories of Markov processes, Uspehi Mat. Nauk 26 (1971), no. 4(160), 153 – 172 (Russian).
[6] E. B. Dynkin, Integral representation of excessive measures and excessive functions, Uspehi Mat. Nauk 27 (1972), no. 1(163), 43 – 80 (Russian). · Zbl 0321.60002
[7] E. B. Dynkin, Sufficient statistics and extreme points, Ann. Probab. 6 (1978), no. 5, 705 – 730. · Zbl 0403.62009
[8] E. B. Dynkin, On duality for Markov processes, Stochastic analysis (Proc. Internat. Conf., Northwestern Univ., Evanston, Ill., 1978) Academic Press, New York-London, 1978, pp. 63 – 77.
[9] G. A. Hunt, Markoff chains and Martin boundaries, Illinois J. Math. 4 (1960), 313 – 340. · Zbl 0094.32103
[10] -, Transformation of Markov processes, Proc. Internat. Congress Math., Stockholm, 1962, pp. 531-535.
[11] Hiroshi Kunita and Takesi Watanabe, Markov processes and Martin boundaries. I, Illinois J. Math. 9 (1965), 485 – 526. · Zbl 0147.16505
[12] S. E. Kuznecov, Construction of Markov processes with random birth and death times, Teor. Verojatnost. i Primenen. 18 (1973), 596 – 601 (Russian, with English summary).
[13] Robert S. Martin, Minimal positive harmonic functions, Trans. Amer. Math. Soc. 49 (1941), 137 – 172. · Zbl 0025.33302
[14] Jacques Neveu, Bases mathématiques du calcul des probabilités, Masson et Cie, Éditeurs, Paris, 1964 (French). · Zbl 0137.11203
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.