Generalized solutions of a class of nuclear-space-valued stochastic evolution equations |
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Authors: | Donald A. Dawson Luis G. Gorostiza |
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Affiliation: | (1) Carleton University, K1S 5B6 Ottawa, Ontario, Canada;(2) Centro de Investigación y de Estudios Avanzados, 07000 México, D. F., México |
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Abstract: | Generalized solutions are defined for stochastic evolution equations of the formdYt =A*Ytdt + dZt on the nuclear triplel(Rd) L2(Rd) l(Rd), whereA does not mapl(Rd) into itself. One case which is treated in detail involvesA = –(–)/2,0 < < 2. This example arises as the Langevin equation for the fluctuation limit of a system of particles migrating according to a symmetric stable process and undergoing critical branching in a random medium.The research of D. A. Dawson was supported by the Natural Sciences and Engineering Research Council of Canada. L. G. Gorostiza's research was supported in part by CONACyT Grants PCEXCNA-040319 and 140102 G203-006, Mexico. |
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