Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

Stochastic convolution in separable Banach spaces and the stochastic linear Cauchy problem

100%

Brzeźniak Z., van Neerven J.

Studia Mathematica

2000

tom 143

nr 1

43-74

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 $X_t = ∫^{t}_{0} S(t-s)BdW_{s}^{H}$.

Ograniczanie wyników

1 Studia Mathematica

1 Brzeźniak Z.

1 van Neerven J.

1 2000

Wyniki wyszukiwania

Stochastic convolution in separable Banach spaces and the stochastic linear Cauchy problem