- Tytuł:
- Stochastic convolution in separable Banach spaces and the stochastic linear Cauchy problem
- Autorzy:
-
Brzeźniak, Zdzisław
van Neerven, Jan - Powiązania:
- https://bibliotekanauki.pl/articles/1205938.pdf
- Data publikacji:
- 2000
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Opis:
- Let H be a separable real Hilbert space and let E be a separable real Banach space. We develop a general theory of stochastic convolution of ℒ(H,E)-valued functions with respect to a cylindrical Wiener process ${W_{t}^{H}}_{t ∈ [0,T]}$ with Cameron-Martin space H. This theory is applied to obtain necessary and sufficient conditions for the existence of a weak solution of the stochastic abstract Cauchy problem (ACP) $dX_t = AX_tdt + BdW_t^H$ (t∈ [0,T]), $X_0 = 0$ almost surely, where A is the generator of a $C_0$-semigroup ${S(t)}_{t ≥ 0}$ of bounded linear operators on E and B ∈ ℒ(H,E) is a bounded linear operator. We further show that whenever a weak solution exists, it is unique, and given by a stochastic convolution $X_t = ∫^{t}_{0} S(t-s)BdW_{s}^{H}$.
- Źródło:
-
Studia Mathematica; 2000, 143, 1; 43-74
0039-3223 - Pojawia się w:
- Studia Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł