Renormalizations of branching random walks in equilibrium

Electronic Journal of Probability

Volumn 7, Issue , 2002, Pages 1-57

  Zähle, Iljana ^a  

^a UNIVERSITY OF ERLANGEN NUREMBERG   (Germany)

Author keywords

Branching random walk; Green s function of random walks; Palm distribution; Renormalization

Indexed keywords

EID: 3943100892     PISSN: None     EISSN: 10836489     Source Type: Journal    
DOI: 10.1214/EJP.v7-106     Document Type: Article

References (16)

1. J. T. Cox and A. Greven. On the long term behavior of some finite particle systems. Probab. Theory Related Fields, 85(2): 195-237, 1990.
2. D. A. Dawson and A. Greven. Multiple space-time scale analysis for interacting branching models. Electron. J. Probab., 1:no. 14, approx. 84 pp. (electronic), 1996.
3. D. A. Dawson, L. G. Gorostiza, and A. Wakolbinger. Occupation time fluctuations in branching systems. J. Theoret. Probab., 14:729-796, 2001.
4. D. A. Dawson and E. A. Perkins. Historical processes. Mem. Amer. Math. Soc., 93(454):iv+179, 1991.
5. R. L. Dobrushin. Gaussian and their subordinated self-similar random generalized fields. Ann. Probab., 7(1):1-28, 1979.
6. E. B. Dynkin. Branching particle systems and superprocesses. Ann. Probab., 19(3):1157-1194, 1991.
7. A. Greven. A phase transition for the coupled branching process. I. The ergodic theory in the range of finite second moments. Probab. Theory Related Fields, 87(4):417-458, 1991.
8. I. M. Gel’fand and N. Ya. Vilenkin. Generalized functions IV: Applications of harmonic analysis. Academic Press, New York and London, 1964.
9. L. G. Gorostiza, S. Roelly, and A. Wakolbinger. Sur la persistance du processus de Dawson-Watanabe stable. l’interversion de la limite en temps et de la renormalisation. In Sem. Prob. XXIV, volume 1426 of Lecture Notes in Mathematics, pages 275-281, Berlin, 1990. SpringerVerlag.
10. L. G. Gorostiza and A. Wakolbinger. Persistence criteria for a class of critical branching particle systems in continuous time. Ann. Probab., 19(1):266-288, 1991.
11. R. A. Holley and D. W. Stroock. Generalized Ornstein-Uhlenbeck processes and infinite particle branching Brownian motions. Publ. Res. Inst. Math. Sci., Kyoto Univ., 14:741-788, 1978.
12. J.-F. Le Gall. Une construction trajectorielle de certains processus de Markov a valeurs mesures. C. R. Acad. Sci. Paris Ser. I Math., 308(18):533-538, 1989.
13. J.-F. Le Gall. Brownian excursions, trees and measure-valued branching processes. Ann. Probab., 19(4):1399-1439, 1991.
14. T. M. Liggett and F. Spitzer. Ergodic theorems for coupled random walks and other systems with locally interacting components. Z. Wahrsch. Verw. Gebiete, 56(4):443-468, 1981.
15. F. Spitzer. Principles of random walk. D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London, 1964. The University Series in Higher Mathematics.
16. I. Zahle. Renormalization of the voter model in equilibrium. Ann. Probab., 29(3):1262-1302, 2001.