GENERALIZED SOLUTIONS FOR STOCHASTIC PROBLEMS IN THE ITO FORM IN GELFAND-SHILOV SPACES

DOI10.14529/mmph160201zbMath1344.47056OpenAlexW2471161341MaRDI QIDQ2810332

V. A. Bovkun

Publication date: 1 June 2016

Published in: Bulletin of the South Ural State University series "Mathematics. Mechanics. Physics" (Search for Journal in Brave)

Full work available at URL: http://mathnet.ru/eng/vyurm293

zbMATH Keywords

Wiener processgeneralized solutionGelfand-Shilov spacesgeneralized Fourier transformstochastic Cauchy problem

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) One-parameter semigroups and linear evolution equations (47D06) Functional-differential equations in abstract spaces (34K30) Ordinary differential equations and systems with randomness (34F05) Linear operators and ill-posed problems, regularization (47A52) Distributions on infinite-dimensional spaces (46F25) Applications of operator theory in probability theory and statistics (47N30)

Cites Work

• Potential \(\text Ш\) for abelian varieties
• Weak and generalized solutions of abstract stochastic equations.
• Abstract stochastic equations. I: Classical and distributional solutions
• Abstract stochastic equations. II: Solutions in spaces of abstract stochastic distributions.
• Stochastic Equations in Infinite Dimensions
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