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Small diffusion and fast dying out asymptotics for superprocesses as non-Hamiltonian quasiclassics for evolution equations
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Kolokoltsov, V. N. (Vasiliĭ Nikitich). (2001) Small diffusion and fast dying out asymptotics for superprocesses as non-Hamiltonian quasiclassics for evolution equations. Electronic Journal of Probability, Vol.6 (No.21). ISSN 1083-6489
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Abstract
The small diffusion and fast dying out asymptotics is calculated for nonlinear evolution equations of a class of superprocesses on manifolds, and the corresponding logarithmic limit of the solution is shown to be given by a solution of a certain problem of calculus of variations with a non-additive (and non-integral) functional.
| Item Type: | Journal Article |
|---|---|
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Faculty of Science > Statistics |
| Library of Congress Subject Headings (LCSH): | Diffusion processes, Manifolds (Mathematics), Asymptotic distribution (Probability theory) |
| Journal or Publication Title: | Electronic Journal of Probability |
| Publisher: | Institute of Mathematical Statistics |
| ISSN: | 1083-6489 |
| Date: | 2001 |
| Volume: | Vol.6 |
| Number: | No.21 |
| Number of Pages: | 16 |
| Status: | Peer Reviewed |
| Publication Status: | Published |
| Access rights to Published version: | Open Access |
| References: | [AHK] S. Albeverio, A. Hilbert, V.N. Kolokoltsov. Sur le comportement asymptotique du noyau associe a une diffusion degeneree. C.R. Math. Rep. Acad. Sci. Canada 22:4 (2000), 151{159. MR [Et] A. Etheridge. An Introduction to Superprocesses. University Lecture Series 20, AMS, Providence, Rhode Island 2000. MR [Joe] E. Joergensen. Construction of the Brownian motion and the Ornstein-Uhlenbeck Process in a Riemannian manifold. Z. Wahrscheinlichkeitstheorie Verw. Gebiete 44 (1978), 71{87. MR80c:60094 [Kl] A. Klenke. Clustering and invariant measures for spatial branching models with infinite variance. Ann. Prob. 26:3 (1998), 1057{1087. MR99i:60160 [Kol1] V. Kolokoltsov. Semiclassical Analysis for Diffusions and Stochastic Processes. Springer Lecture Notes Math., v. 1724, 2000. MR2001f:58073 [Kol2] V. Kolokoltsov. On Linear, Additive, and Homogeneous Operators. In: V. Maslov, S. Samborski (Eds.) Idempotent Analysis. Advances in Soviet Mathematics 13, 1992, 87{101. MR93k:47065 [KM] V. Kolokoltsov, V.P. Maslov. Idempotent Analysis and its Applications. Kluwer Academic 1997. MR97d:49031 [Ma1] V.P. Maslov. Perturbation Theory and Asymptotical Methods. Moscow, MGU 1965 (in Russian). French translation Paris, Dunod, 1972. MR(not reviewed) [Ma2] V.P. Maslov. Complex Markov chains and Feynman path integral. Moscow, Nauka, 1976 (in Russian). MR57:18574 [Pu] A. Puchalskii. Large deviation of semimartingales: a maxingale approach. Stochastics and Stochastics Reports 61 (1997), 141{243. MR98h:60033 [Sm] J. Smoller. Shock Waves and Reaction-Diffusion Equations. Springer-Verlag, 1983. MR84d:35002 [Var1] 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. MR34:8001 [Var2] S.R. Varadhan. Diffusion Processes in a Small Time Interval. Comm. Pure Appl. Math. 20 (1967), 659{685. MR36:970 [Var3] S.R. Varadhan. Scaling limits for interacting diffusions. Comm. Math. Phys. 135 (1991), 331{353. MR92e:60195 |
| URI: | http://wrap.warwick.ac.uk/id/eprint/39396 |
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