Natural linear additive functionals of superprocesses

Annals of Probability

Volumn 25, Issue 2, 1997, Pages 640-661

  Dynkin, E B ^a   Kuznetsov, S E ^b  

^a Cornell University ^*  (United States)

^b CENTRAL ECONOMICS AND MATHEMATICS INSTITUTE   (Russian Federation)

Author keywords

Branching; Log potentials; Measure valued processes; Natural linear additive functionals; Potentials

Indexed keywords

EID: 0031487162     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/aop/1024404414     Document Type: Article

References (23)

1. ADAMS, D. R. and HEDBERG, L. I. (1996). Function Spaces and Potential Theory. Springer, Berlin.
2. DAWSON, D. A. and PERKINS, E. A. (1991). Historical processes. Mem. Amer. Math. Soc. 454.
3. DELLACHERIE, C. and MEYER, P.-A. (1987). Probabilités et Potentiel. Hermann, Paris.
4. DYNKIN, E. B. (1993). Superprocesses and partial differential equations. Ann. Probab. 21 1185-1262.
5. DYNKIN, E. B. (1994). An Introduction to Branching Measure-Valued Processes. Amer. Math. Soc., Providence, RI.
6. DYNKIN, E. B. (1989). Superprocesses and their linear additive functionals. Trans. Amer. Math. Soc. 314 255-282.
7. DYNKIN, E. B. (1991). Path processes and historical Superprocesses. Probab. Theory Related Fields 9089-115.
8. DYNKIN, E. B. (1991). Additive functional of superdiffusion processes. In Random Walks, Brownian Motion and Interacting Particle Systems (R. Durrett and H. Kesten, eds.) 269-281. Birkhäuser, Boston.
9. DYNKIN, E. B. (1992). Superdiffusions and parabolic nonlinear differential equations. Ann. Probab. 20 942-962.
10. DYNKIN, E. B. (1993). Birth delay of a Markov process and the stopping distributions for regular processes. Probab. Theory Related Fields 94 399-411.
11. DYNKIN, E. B. and KUZNETSOV, S. E. (1974). Determining functions of Markov processes and corresponding dual regular classes. Dokl. Akad. Nauk SSSR 414 25-28. [English translation in Soviet Math. Dokl. (1974) 15.]
12. DYNKIN, E. B. and KUZNETSOV, S. E. (1974). Determining functions of Markov processes and corresponding dual regular classes. Dokl. Akad. Nauk SSSR 414 25-28. [English translation in Soviet Math. Dokl. (1974) 15.]
13. DYNKIN, E. B. and KUZNETSOV, S. E. (1996). Linear additive functionals of superdiffusions and related nonlinear P.D.E. Trans. Amer. Math. Soc. 348 1959-1987.
14. α dominated by L-harmonic functions. J. Analyse Math. 68 15-37.
15. DYNKIN, E. B. and KUZNETSOV, S. E. (1996). Superdiffusions and removable singularities for quasilinear partial differential equations. Comm. Pure Appl. Math. 49 125-176.
16. DYNKIN, E. B. and KUZNETSOV, S. E. (1997). Nonlinear parabolic P.D.E. and additive functionals of superdiffusions. Ann. Probab. 25 662-701.
17. DYNKIN, E. B., KUZNETSOV, S. E. and SKOROKHOD, A. V. (1994). Branching measure-valued processes. Probab. Theory Related Fields 99 55-96.
18. FITZSIMMONS, P. J. (1988). Construction and regularity of measure-valued Markov branching processes. Israel J. Math. 64 337-361.
19. ISCOE, I. (1986). A weighted occupation time for a class of measure-valued branching processes. Probab. Theory Related Fields 71 85-116.
20. ISCOE, I. (1986). Ergodic theory and local occupation time for measure-valued critical branching Brownian motion. Stochasticis 18 197-243.
21. KUZNETSOV, S. E. (1974). Construction of Markov processes with random birth and death. Theory Probab. Appl. 18 571-574.
22. KUZNETSOV, S. E. (1994). Regularity properties of a supercritical superprocess. In The Dynkin Festschrift: Markov Processes and Their Applications (Mark I. Freidlin, ed.) 221-236. Birkhäuser, Boston.
23. 2 in a domain. Probab. Theory Related Fields 102 393-432.