Geodesic
Generalized solutions to stochastic systems in Gelfand-Shilov spaces
Novi Sad Journal of Mathematics, Tome 45 (2015) no. 2.

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The Cauchy problem for systems of differential equations with multiplicative random perturbations in the form of infinite-dimensional Ito integrals is studied. For the systems correct by Petrovskii, conditionally correct and incorrect we point out Gelfand-Shilov spaces of generalized functions where a generalized solution coincides with a mild solution.
Publié le :
DOI : 10.30755/NSJOM.03468
Classification : 46F25, 47D06, 34K30, 60H40
Keywords: generalized function, $R$-semigroup, Wiener process, Ito integral, multiplier, convolution 
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     author = {Irina V. Melnikova and Uliana Alekseeva},
     title = {Generalized solutions to stochastic systems
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     journal = {Novi Sad Journal of Mathematics},
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Irina V. Melnikova; Uliana Alekseeva. Generalized solutions to stochastic systems
in Gelfand-Shilov spaces. Novi Sad Journal of Mathematics, Tome 45 (2015) no. 2. doi : 10.30755/NSJOM.03468. http://geodesic.mathdoc.fr/articles/10.30755/NSJOM.03468/

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