Abstract
Generalized solutions are defined for stochastic evolution equations of the formdY t =A * Y t dt + dZ t on the nuclear triplel(R d) ⊂ L2(R d) ⊂l′(R d), whereA does not mapl(R d) into itself. One case which is treated in detail involvesA = −(−Δ)α/2,0 < α < 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.
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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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Dawson, D.A., Gorostiza, L.G. Generalized solutions of a class of nuclear-space-valued stochastic evolution equations. Appl Math Optim 22, 241–263 (1990). https://doi.org/10.1007/BF01447330
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DOI: https://doi.org/10.1007/BF01447330