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Let $H_B$ be the reproducing kernel Hilbert space (RKHS) of the Brownian Motion $(B_t)$ on $[0,1]$. It is well known that with probability 1 the paths of $(B_t)$ are not contained in $H_B$. But is ...

I feel confused with a particular step in the $L^2$ consturction of Brownian motion. Let $\{\xi_n \sim N(0,1)\}_{n\geq 1}$ be a sequence of i.i.d Gaussian random variables on some probability space $(\...

Cross-posted from: "https://math.stackexchange.com/questions/3917971/malliavin-derivative-of-stopped-brownian-motion" I have a small question concerning the Malliavin derivatives. It could ...

Let$^1$ $T>0$ $U,H$ be separable $\mathbb R$-Hilbert spaces $Q\in\mathfrak L(U)$ be nonnegative and self-adjoint operator with finite trace $\operatorname{tr}Q$ $(e^n)_{n\in\mathbb N}$ be an ...

The Brownian motion has the following (Levy-Ciesielski?) construction via Hilbert space isomorphisms: Let $\{ Z_i \}_{i \in \mathbb{Z}}$ be i.i.d. $N(0,1)$ random variables defined on $(\Omega, \...