Small diffusion and fast dying out asymptotics for superprocesses as non-hamiltonian quasiclassics for evolution equations

Electronic Journal of Probability

Volumn 6, Issue , 2001, Pages 1-16

  Kolokol’tsov, Vassili N ^a  

^a NOTTINGHAM TRENT UNIVERSITY   (United Kingdom)

Author keywords

Curvilinear Ornstein Uhlenbeck process; Dawson Watanabe superprocess; Logarithmic limit; Reaction diffusion equation; Small diffusion asymptotics

Indexed keywords

EID: 0042241231     PISSN: None     EISSN: 10836489     Source Type: Journal    
DOI: 10.1214/EJP.v6-94     Document Type: Article

References (14)

1. S. Albeverio, A. Hilbert, V.N. Kolokoltsov. Sur le comportement asymptotique du noyau associé à une diffusion degenerée. C.R. Math. Rep. Acad. Sci. Canada 22:4 (2000), 151-159.
2. A. Etheridge. An Introduction to Superprocesses. University Lecture Series 20, AMS, Providence, Rhode Island 2000. MR
3. E. Joergensen. Construction of the Brownian motion and the Ornstein-Uhlenbeck Process in a Rie-mannian manifold. Z. Wahrscheinlichkeitstheorie Verw. Gebiete 44 (1978), 71-87.
4. A. Klenke. Clustering and invariant measures for spatial branching models with infinite variance. Ann. Prob. 26:3 (1998), 1057-1087.
5. V. Kolokoltsov. Semiclassical Analysis for Diffusions and Stochastic Processes. Springer Lecture Notes Math., v. 1724, 2000.
6. V. Kolokoltsov. On Linear, Additive, and Homogeneous Operators. In: V. Maslov, S. Samborski (Eds.) Idempotent Analysis. Advances in Soviet Mathematics 13, 1992, 87-101.
7. V. Kolokoltsov, V.P. Maslov. Idempotent Analysis and its Applications. Kluwer Academic 1997.
8. V.P. Maslov. Perturbation Theory and Asymptotical Methods. Moscow, MGU 1965 (in Russian). French translation Paris, Dunod, 1972. MR(not reviewed)
9. V.P. Maslov. Complex Markov chains and Feynman path integral. Moscow, Nauka, 1976 (in Russian).
10. A. Puchalskii. Large deviation of semimartingales: a maxingale approach. Stochastics and Stochastics Reports 61 (1997), 141-243.
11. J. Smoller. Shock Waves and Reaction-Diffusion Equations. Springer-Verlag, 1983.
12. S.R. Varadhan. On the behavior of the fundamental solution of the heat equation with variable coefficients. Comm. Pure Appl. Math. 20 (1967), 431-455.
13. S.R. Varadhan. Diffusion Processes in a Small Time Interval. Comm. Pure Appl. Math. 20 (1967), 659-685.
14. S.R. Varadhan. Scaling limits for interacting diffusions. Comm. Math. Phys. 135 (1991), 331-353.