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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 ...

The Setup Let $\xi_t$ be a process adapted to the filtration $\mathfrak{F_t}$ of the semi-martinagale $X_t$, such that both are square integrable. Then is the map \begin{align} F_T: L^2(\mathfrak{...

Let $P:\ell^1(\mathbb{Z}^d) \rightarrow \ell^1(\mathbb{Z}^d)$ be given by $$(Pz)(x)=\sum_{y \tilde \ x} \frac{1}{2d} z(y)$$ where the tilde indicates that $y$ is a neighboured vertex of $x.$ I ...

Let $U$ be a separable $\mathbb R$-Hilbert space and $W$ be a $Q$-Wiener process on a complete and right-continuous filtered probability space. Let $H$ be a separable $\mathbb R$-Hilbert space and $X$ ...

Let $H$ be a separable $\mathbb R$-Hilbert space $(e_n)_{n\in\mathbb N}$ be an orthonormal basis of $H$ $(\Omega,\mathcal A,\operatorname P)$ be a probability space $(\mathcal F_t)_{t\ge0}$ be a ...