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Remark: Even when this question is about stochastic PDEs, it can be answered by someone who has no knowledge about probability theory or PDEs. I'm reading Stochastic Differential Equations in ...

Consider a Stratonovich SPDE $$X_t=X_0+\int_0^tb(s,X_s)\:{\rm d}s+\int_0^t\sigma(s,X_s)\circ{\rm d}W_s\tag 1$$ in a separable $\mathbb R$-Hilbert space $H$ with $W$ being a $Q$-Wiener process on a ...

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 $\...

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 $(\Omega,\mathcal A,(\mathcal F_t)_{t\in[0,\:T]},\operatorname P)$ be a filtered probability space $U,H$ be separable $\mathbb R$-Hilbert spaces $(e_n)_{n\in\mathbb N}$ and $(f_n)_{n\in\mathbb N}$...