Homogeneous random measures and strongly supermedian kernels of a markov process

Electronic Journal of Probability

Volumn 8, Issue , 2003, Pages 1-54

  Fitzsimmons, P J ^a   Getoor, R K ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Additive functional; Characteristic measure; Homogeneous random measure; Kuznetsov measure; Potential kernel; Smooth measure; Strongly supermedian

Indexed keywords

EID: 10644225857     PISSN: None     EISSN: 10836489     Source Type: Journal    
DOI: 10.1214/EJP.v8-142     Document Type: Article

References (46)

1. Âzéma, J.: Noyau potentiel associe à une fonction excessive d’un processus de Markov. Ann. Inst. Fourier (Grenoble) 19 (1969) 495-526.
2. Âzéma, J.: Une remarque sur les temps de retour. Trois applications. In Séminaire de Probabilités, VI. Springer, Berlin, 1972, pp. 35-50. Lecture Notes in Math., Vol. 258.
3. Âzéma, J.:: Theorie generale des processus et retournement du temps. Ann. Sci. École Norm. Sup. (4) 6 (1973) 459-519.
4. Béznéa, L., and Boboc, N.: Feyel’s techniques on the supermedian functionals and strongly supermedian functions. Potential Anal. 10 (1999) 347-372.
5. Béznéa, L., and Boboc, N.: Excessive kernels and Revuz measures. Probab. Theory Related Fields 117 (2000) 267-288.
6. Béznéa, L., and Boboc, N.: Smooth measures and regular strongly supermedian kernels generating sub-Markovian resolvents. Potential Anal. 15 (2001) 77-87.
7. Béznéa, L., and Boboc, N.: Strongly supermedian kernels and Revuz measures. Ann. Probab. 29 (2001) 418-436.
8. Beznea, L., and Bobüc, N.: Fine densities for excessive measures and the Revuz correspondence. Preprint (2002).
9. Blümenthal, R.M. and Getüür, R.K.: Markov Processes and Potential Theory. Academic Press, New York, 1968.
10. Dellacherie, C.: Capacités et Processus Stochastiques. Springer-Verlag, Berlin, 1972.
11. Dellacherie, C.: Autour des ensembles semi-polaires. In Seminar on Stochastic Processes, 1987. Birkhâuser Boston, Boston, MA, 1988, pp. 65-92.
12. Dellacherie, C. and Meyer, P.-A.: Probabilités et Potentiel. Chapitres V a VIII. Hermann, Paris, 1980. Theorie des martingales.
13. Dellacherie, C. and Meyer, P.-A.: Probabilités et Potentiel. Chapitres IX a XI. Hermann, Paris, 1983. Theorie discrete du potential.
14. Dellacherie, C. and Meyer, P.-A.: Probabilites et Potentiel. Chapitres XII-XVI. Hermann, Paris, 1987. Theorie du potentiel associee a une résolvante. Theorie des processus de Markov.
15. Dellacherie, C., Meyer, P.-A. and Maisonneuve, B.: Probabilites et Potentiel. Chapitres XVII-XXIV. Hermann, Paris, 1992. Processus de Markov (fin), Complements de calcul stochastique.
16. Düncan, R.D. and getüür, R.K.: Equilibrium potentials and additive functionals. Indiana Univ. Math. J. 21 (1971/1972) 529-545.
17. Dynkin, E.B.: Markov Processes, Vols. I, II. Academic Press, New York, 1965.
18. Dynkin, E.B.: Additive functionals of Markov processes and stochastic systems. Ann. Inst. Fourier (Grenoble) 25 (1975) 177-200.
19. Dynkin, E.B.: Markov systems and their additive functionals. Ann. Probab. 5 (1977) 653-677.
20. Feyel, D.: Representation des fonctionnelles surmedianes. Z. Wahrsch. verw. Gebiete 58 (1981) 183-198.
21. Feyel, D.: Sur la theorie fine du potentiel. Bull. Soc. Math. France 111 (1983) 41-57.
22. Fitzsimmons, P.J.: Homogeneous random measures and a weak order for the excessive measures of a Markov process. Trans. Amer. Math. Soc. 303 (1987) 431-478.
23. Fitzsimmons, P.J.: Markov processes and nonsymmetric Dirichlet forms without regularity. J. Funct. Anal. 85 (1989) 287-306.
24. Fitzsimmons, P.J. and Getüür, R.K.: A fine domination principle for excessive measures. Math. Z. 207 (1991) 137-151.
25. Fitzsimmons, P.J. and Getüür, R.K.: A weak quasi-Lindelâf property and quasi-fine supports of measures. Math. Ann. 301 (1995) 751-762.
26. Fitzsimmons, P.J. and Getoür, R.K.: Smooth measures and continuous additive functionals of right Markov processes. In Ito’s Stochastic Calculus and Probability Theory. Springer, Tokyo, 1996, pp. 31-49.
27. Fükushima, M., Oshima, Y., and Takeda, M.: Dirichlet Forms and Symmetric Markov Processes. Walter de Gruyter & Co., Berlin, 1994.
28. Getoür, R.K.: Excessive Measures. Birkhâuser, Boston, 1990.
29. Getoür, R.K.: Measures not charging semipolars and equations of Schrâdinger type. Potential Anal. 4 (1995) 79-100.
30. Getoür, R.K.: Measure perturbations of Markovian semigroups. Potential Anal. 11 (1999) 101-133.
31. [GS74 Getoür, R.K. and Sharpe, M.J.: Balayage and multiplicative functionals. Z. Wahrsch. verw. Gebiete 28 (1973/74) 139-164.
32. Getoür, R.K. and Sharpe, M.J.: Naturality, standardness, and weak duality for Markov processes. Z. Wahrsch. verw. Gebiete 67 (1984) 1-62.
33. Hirsch, F.: Conditions necessaires et suffisantes d’existence de résolvantes. Z. Wahrsch. verw. Gebiete 29 (1974) 73-85.
34. Hunt, G.A.: Markoff processes and potentials. I, II. Illinois J. Math. 1 (1957) 44-93, 316-369.
35. Mertens, J.-F.: Strongly supermedian functions and optimal stopping. Z. Wahrsch. verw. Gebiete 26 (1973) 119-139.
36. Meyer, P.-A.: Fonctionelles multiplicatives et additives de Markov. Ann. Inst. Fourier (Grenoble) 12 (1962) 125-230.
37. Mokobüdzki, G.: Compactification relative à la topologie fine en theorie du potentiel. In Théorie du potentiel (Orsay, 1983). Springer, Berlin, 1984, pp. 450-473.
38. Revuz, D.: Mesures associees aux fonctionnelles additives de Markov. I. Trans. Amer. Math. Soc. 148 (1970) 501-531.
39. Revuz, D.: Mesures associees aux fonctionnelles additives de Markov. II. Z. Wahrsch. verw. Gebiete 16 (1970) 336-344.
40. Revuz, D.: The stopping distributions of a Markov Process. Invent. Math. 14 (1971) 1-16.
41. Sharpe, M.J.: Exact multiplicative functionals in duality. Indiana Univ. Math. J. 21 (1971/72) 27-60.
42. Sharpe, M.: General Theory of Markov Processes. Academic Press, Boston, 1988.
43. Sur, M.G.: Continuous additive functionals of Markov processes and excessive functions. Soviet Math. Dokl. 2 (1961) 365-368.
44. Taylor, J.C.: On the existence of sub-Markovian resolvents. Invent. Math. 17 (1972) 85-93.
45. Taylor, J.C.: A characterization of the kernel limôV\ for sub-Markovian resolvents (V\). Ann. Probab. 3 (1975) 355-357.
46. Volkonskii, V.A.: Additive functionals of Markov processes. Trudy Moskov. Mat. Obsc. 9 (1960) 143-189.