Abstract:
We study the existence, uniqueness, and stability of a solution to the Cauchy problem for a stochastic differential equation with multiplicative noise in the spaces of generalized random variables with values in a Hilbert space.
Keywords:
Cauchy problem, semigroup, white noise, generalized solutions.
Citation:
I. V. Melnikova, M. A. Alshanskiy, “The generalized well-posedness of the Cauchy problem for an abstract stochastic equation with multiplicative noise”, Trudy Inst. Mat. i Mekh. UrO RAN, 18, no. 1, 2012, 251–267; Proc. Steklov Inst. Math. (Suppl.), 280, suppl. 1 (2013), 134–150
\Bibitem{MelAls12}
\by I.~V.~Melnikova, M.~A.~Alshanskiy
\paper The generalized well-posedness of the Cauchy problem for an abstract stochastic equation with multiplicative noise
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2012
\vol 18
\issue 1
\pages 251--267
\mathnet{http://mi.mathnet.ru/timm794}
\elib{https://elibrary.ru/item.asp?id=17358693}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2013
\vol 280
\issue , suppl. 1
\pages 134--150
\crossref{https://doi.org/10.1134/S0081543813020119}
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Linking options:
https://www.mathnet.ru/eng/timm794
https://www.mathnet.ru/eng/timm/v18/i1/p251
This publication is cited in the following 7 articles:
E. V. Bychkov, A. V. Bogomolov, K. Yu. Kotlovanov, “Stochastic mathematical model of internal waves”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 13:2 (2020), 33–42
E. V. Bychkov, N. N. Soloveva, G. A. Sviridyuk, “Matematicheskaya model akusticheskikh voln v ogranichennoi oblasti s «belym shumom»”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 11:3 (2019), 12–19
Maxim A. Alshanskiy, “A model of age-structured population under stochastic perturbation of death and birth rates”, Ural Math. J., 4:1 (2018), 3–13
I. V. Melnikova, M. A. Alshanskiy, “Stochastic equations with an unbounded operator coefficient and multiplicative noise”, Siberian Math. J., 58:6 (2017), 1052–1066
M. A. Alshanskii, “Integraly Ito i Khitsudy–Skorokhoda v beskonechnomernom sluchae”, Sib. elektron. matem. izv., 11 (2014), 185–199
I. V. Melnikova, M. A. Alshanskiy, “White noise calculus in applications to stochastic equations in Hilbert spaces”, Journal of Mathematical Sciences, 218:4 (2016), 395–429
M. A. Alshanskiy, “Wiener-Itô Chaos Expansion of Hilbert Space Valued Random Variables”, Journal of Probability, 2014 (2014), 1
Citation in format AMSBIB
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