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Small diffusion and fast dying out asymptotics for superprocesses as non-Hamiltonian quasiclassics for evolution equations. (English) Zbl 0981.60065

Summary: The small diffusion and fast dying out asymptotics is calculated for nonlinear 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.

MSC:

60J25 Continuous-time Markov processes on general state spaces
60F10 Large deviations
35K57 Reaction-diffusion equations
49L99 Hamilton-Jacobi theories
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