Geodesic
Connection between weak and generalized solutions of infinite-dimensional stochastic problems
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2014), pp. 12-27

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We investigate the stochastic Cauchy problem for the first order equation with singular white noise and generators of regularized (integrated, convoluted) semigroups in Hilbert spaces and abstract distribution spaces. Weak solutions for the problem in the Ito form and generalized solutions for the differential problem in abstract distribution spaces are constructed in dependence on properties of the generator. Connections between these solutions are shown.
Mots-clés : distribution
Keywords: semigroup of operators, white noise, Wiener process, generalized solution, weak solution, regularized solution. 
@article{IVM_2014_5_a1,
     author = {I. V. Mel'nikova and O. S. Starkova},
     title = {Connection between weak and generalized solutions of infinite-dimensional stochastic problems},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {12--27},
     publisher = {mathdoc},
     number = {5},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2014_5_a1/}
}
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I. V. Mel'nikova; O. S. Starkova. Connection between weak and generalized solutions of infinite-dimensional stochastic problems. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2014), pp. 12-27. http://geodesic.mathdoc.fr/item/IVM_2014_5_a1/