Stochastic differential equations in a Banach space driven by the cylindrical Wiener process
| Autor: | Badri Mamporia |
|---|---|
| Jazyk: | angličtina |
| Předmět: |
Stratonovich integral
Wiener processes lcsh:Mathematics General Mathematics 010102 general mathematics Mathematical analysis Integral representation theorem for classical Wiener space Covariance operators in Banach spaces lcsh:QA1-939 Malliavin calculus 01 natural sciences Stochastic partial differential equation 010104 statistics & probability Stochastic differential equation Ito stochastic integrals and stochastic differential equations Classical Wiener space Paley–Wiener integral 0101 mathematics C0-semigroup Mathematics |
| Zdroj: | Transactions of A. Razmadze Mathematical Institute, Vol 171, Iss 1, Pp 76-89 (2017) |
| ISSN: | 2346-8092 |
| DOI: | 10.1016/j.trmi.2016.10.003 |
| Popis: | Generalized stochastic integral from predictable operator-valued random process with respect to a cylindrical Wiener process in an arbitrary Banach space is defined. The question of existence of the stochastic integral in a Banach space is reduced to the problem of decomposability of the generalized random element. The sufficient condition of existence of the stochastic integral in terms of p-absolutely summing operators is given. The stochastic differential equation for generalized random processes is considered and existence and uniqueness of the solution is developed. As a consequence, the corresponding results of the stochastic differential equations in an arbitrary Banach space are given. Keywords: Ito stochastic integrals and stochastic differential equations, Wiener processes, Covariance operators in Banach spaces |
| Databáze: | OpenAIRE |
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