All Questions

Let $T>0$ $d\in\mathbb N$ $\Lambda\subseteq\mathbb R^d$ be bounded and open $\mathcal V:=\left\{v\in C_c^\infty(\Lambda)^d:\nabla\cdot v=0\right\}$, $$V:=\overline{\mathcal V}^{\left\|\;\cdot\;\...

Let's consider the SDE $${\rm d}X_t=u_t(X_t){\rm d}t+\xi_t(X_t){\rm d}W_t\;\;\;\text{for all }t\ge 0\tag 1$$ where $U,H$ are separable $\mathbb R$-Hilbert spaces $Q\in\mathfrak L(U)$ is nonnegative ...

Let $U,H$ be separable $\mathbb R$-Hilbert spaces $Q\in\mathfrak L(U)$ be nonnegative and self-adjoint with finite trace $U_0:=Q^{1/2}U$ $(\Omega,\mathcal A,(\mathcal F_t)_{t\ge 0},\operatorname P)$ ...

I'm reading the paper On the relation between the Itō and Stratonovich integrals in Hilbert spaces and there is something I don't understand. In the notation of the paper, let $H,H_1$ be separable $\...

I am working through a text on Numerics for SPDEs and there the concept an interpolation (Hilbert-)space associated to an operator is used. To be specific: Definition. Let $H$ be an $\mathbb{R}$-...