Stochastic Cauchy problems in infinite dimensions : generalized and regularized solutions /: generalized and regularized solutions. (2018)

• Record Type: Book
• Further Information: Note: Irina V. Melnikova, Alexei Filinkov.
• Authors: Melʹnikova, I. V (Irina Valerianovna); Filinkov, A. I (Alekseĭ Ivanovich)
• Contents: Well-Posed and Ill-Posed Abstract Cauchy Problems. The Concept of Regularization; Semi-group methods for construction of exact, approximated, and regularized solutions; The Cauchy problem and strongly continuous semi-groups of solution operators; The Cauchy problem with generators of regularized semigroups: integrated, convoluted, and R -semi-groups; R -semi-groups and regularizing operators in the construction of approximated solutions to ill-posed problems Distribution methods for construction of generalized solutions to ill-posed Cauchy problems; Solutions in spaces of abstract distributions; Solutions in spaces of abstract ultra-distributions; Solutions to the Cauchy problem for differential systems in Gelfand–Shilov spaces Examples. Supplements; Examples of regularized semi-groups and their generators; Examples of solutions to Petrovsky correct, conditionally correct and incorrect systems; Definitions and properties of spaces of test functions; Generalized Fourier and Laplace transforms. Structure theorems Infinite-Dimensional Stochastic Cauchy Problems; Weak, regularized, and mild solutions to Itô integrated stochastic Cauchy problems in Hilbert spaces; Hilbert space valued variables, processes, and stochastic integrals. Main properties and results; Solutions to Cauchy problems for equations with additive noise and generators of regularized semi-groups; Solutions to Cauchy problems for semi-linear equations with multiplicative noise; Extension of the Feynman–Kac theorem to the case of relations between stochastic equations and PDEs in Hilbert spaces Infinite-dimensional stochastic Cauchy problems with white noise processes in spaces of distributions; Generalized solutions to linear stochastic Cauchy problems with generators of regularized semi-groups; Quasi-linear stochastic Cauchy problem in abstract Colombeau spaces Infinite-dimensional extension of white noise calculus with application to stochastic problems; Spaces of Hilbert space valued generalized random variables: (S )−ρ (H). Basic examples; Analysis of (S )−ρ (H)-valued processes; S-transform and Wick product. Hitsuda–Skorohod integral. Main properties. Connection with Itô integral; Generalized solutions to stochastic Cauchy problems in spaces of abstract stochastic distributions
• Publisher Details: Place of publication not identified : Chapman and Hall/CRC
• Publication Date: 2018
• Extent: 1 online resource (286 pages)
• Subjects: 519.22; Stochastic differential equations; Infinite dimensional Lie algebras; Cauchy problem
• Languages: English
• ISBNs: 9781315360263; 1315360268
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.