This article is cited in 8 papers

The linear Sobolev-type Equations With Relatively $p$-bounded Operators and Additive White Noise

S. A. Zagrebina, E. A. Soldatova

South Ural State University (National Research University), 76, Lenin Ave, Chelyabinsk, 454080

Abstract: In the paper we observe the Cauchy–Dirichlet problem for the Barenblatt–Zheltov–Kochina equation for the perturbed white noise. We show the reduction of the problem under consideration to the Cauchy problem for stochastic Sobolev-type equation. We obtain sufficient conditions for the unique solvability for the abstract problem and for the Cauchy–Dirichlet problem for the Barenblatt–Zheltov–Kochina equation of the perturbed white noise. Our research is based on the mathematical model of Shestakov–Sviridyuk stochastic optimal measurement where under the «White noise» is understood the Nelson–Gliklikh derivative of the Wiener process.

Keywords: linear Sobolev type equations, relative spectrum, Wiener process, additive white noise.

UDC: 518.517