Kolokol’tsov, Vassili N. Small diffusion and fast dying out asymptotics for superprocesses as non-Hamiltonian quasiclassics for evolution equations. (English) Zbl 0981.60065 Electron. J. Probab. 6, Paper No. 21, 16 p. (2001). 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 Keywords:Dawson-Watanabe superprocess; reaction diffusion equation; logarithmic limit; small diffusion asymptotics; curvilinear Ornstein-Uhlenbeck process PDFBibTeX XMLCite \textit{V. N. Kolokol'tsov}, Electron. J. Probab. 6, Paper No. 21, 16 p. (2001; Zbl 0981.60065) Full Text: EuDML EMIS