A family of L 2-spaces associated to the jumps of a Markov process
Valentin Grecea
Open Mathematics, Tome 9 (2011), p. 709-714 / Harvested from The Polish Digital Mathematics Library

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.

Publié le : 2011-01-01
EUDML-ID : urn:eudml:doc:269579
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     author = {Valentin Grecea},
     title = {A family of L 2-spaces associated to the jumps of a Markov process},
     journal = {Open Mathematics},
     volume = {9},
     year = {2011},
     pages = {709-714},
     zbl = {1233.31007},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0024-0}
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Valentin Grecea. A family of L 2-spaces associated to the jumps of a Markov process. Open Mathematics, Tome 9 (2011) pp. 709-714. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0024-0/

[1] Benveniste A., Jacod J., Systèmes de Lévy des processus de Markov, Invent. Math., 1973, 21(3), 183–198 http://dx.doi.org/10.1007/BF01390195 | Zbl 0265.60074

[2] Dellacherie C., Meyer P.-A., Probabilités et Potentiel, Chapters I–IV, V–VIII, XII–XVI, Actualités Sci. Indust., 1372, 1385, 1417, Hermann, Paris, 1975, 1980, 1987

[3] Dynkin E.B., Additive functionals of a Wiener process determined by stochastic integrals, Teor. Verojatnost. i Primenen., 1960, 5, 441–452 (in Russian) | Zbl 0248.60056

[4] Getoor R.K., Markov Processes: Ray Processes and Right Processes, Lecture Notes in Math., 440, Springer, Berlin-New York, 1975 | Zbl 0299.60051

[5] Kunita H., Watanabe S., On square integrable martingales, Nagoya Math. J., 1967, 30, 209–245 | Zbl 0167.46602

[6] Venttsel A.D., Nonnegative additive functionals of Markov processes, Dokl. Akad. Nauk SSSR, 1961, 137, 17–20 (in Russian)