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

• Autorzy: Valentin Grecea
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Additive functional; Purely discontinuous martingale; Nonbranching point; Totally inaccessible jump

Kategorie tematyczne

• 60J45: Probabilistic potential theory
• 60J25: Continuous-time Markov processes on general state spaces
• 31D05: Axiomatic potential theory

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2011
• Tom: 9
• Numer: 3
• Strony: 709-714

Daty

wydano

2011-06-01

online

2011-03-22

Twórcy

autor

Valentin Grecea

• Institute of Mathematics of the Romanian Academy

Bibliografia

• [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
• [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)
• [4] Getoor R.K., Markov Processes: Ray Processes and Right Processes, Lecture Notes in Math., 440, Springer, Berlin-New York, 1975
• [5] Kunita H., Watanabe S., On square integrable martingales, Nagoya Math. J., 1967, 30, 209–245
• [6] Venttsel A.D., Nonnegative additive functionals of Markov processes, Dokl. Akad. Nauk SSSR, 1961, 137, 17–20 (in Russian)

Identyfikatory

DOI

10.2478/s11533-011-0024-0