Autor: Brzeźniak, Zdzisław - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Space-time continuous solutions to SPDEs driven by a homogeneous Wiener process
Autorzy:: Brzeźniak, Zdzisław
Peszat, Szymon
Powiązania:: https://bibliotekanauki.pl/articles/1216167.pdf
Data publikacji:: 1999
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: stochastic partial differential equations in $L^q$-spaces
homogeneous Wiener process
random environment
stochastic integration in Banach spaces
Opis:: Stochastic partial differential equations on $ℝ^d$ are considered. The noise is supposed to be a spatially homogeneous Wiener process. Using the theory of stochastic integration in Banach spaces we show the existence of a Markovian solution in a certain weighted $L^q$-space. Then we obtain the existence of a space continuous solution by means of the Da Prato, Kwapień and Zabczyk factorization identity for stochastic convolutions.
Źródło:: Studia Mathematica; 1999, 137, 3; 261-299
0039-3223
Pojawia się w:: Studia Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

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

Skocz do pozycji: 3.

Tytuł:: A quantitative asymptotic theorem for contraction semigroups with countable unitary spectrum
Autorzy:: J. K. Batty, Charles
Brzeźniak, Zdzisław
Greenfield, David
Powiązania:: https://bibliotekanauki.pl/articles/1221049.pdf
Data publikacji:: 1996
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: contraction semigroup
unitary spectrum
unitary eigenvector trajectory
asymptotic stability
trivially asymptotically stable
countable
spectral synthesis
Opis:: Let T be a semigroup of linear contractions on a Banach space X, and let $X_{s}(T) = {x ∈ X : lim_{s→∞} ∥T(s)x∥ = 0}$. Then $X_{s}(T)$ is the annihilator of the bounded trajectories of T*. If the unitary spectrum of T is countable, then $X_{s}(T)$ is the annihilator of the unitary eigenvectors of T*, and $lim_{s} ∥T(s)x∥ = inf{∥x-y∥ : y ∈ X_{s}(T)}$ for each x in X.
Źródło:: Studia Mathematica; 1996, 121, 2; 167-183
0039-3223
Pojawia się w:: Studia Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

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