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Connection between weak and generalized solutions to infinite-dimensional stochastic problems

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Abstract

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” problemin abstract distribution spaces are constructed in dependence on properties of the generator. We show connections between these solutions.

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Authors and Affiliations

  1. Ural Federal University, pr. Lenina 51, Ekaterinburg, 620083, Russia

    I. V. Mel’nikova & O. S. Starkova

Authors
  1. I. V. Mel’nikova
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  2. O. S. Starkova
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Corresponding author

Correspondence to I. V. Mel’nikova.

Additional information

Original Russian Text © I.V. Mel’nikova, O.S. Starkova, 2014, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2014, No. 5, pp. 12–27.

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Mel’nikova, I.V., Starkova, O.S. Connection between weak and generalized solutions to infinite-dimensional stochastic problems. Russ Math. 58, 8–20 (2014). https://doi.org/10.3103/S1066369X14050028

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  • DOI: https://doi.org/10.3103/S1066369X14050028

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