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Assume we have a Hida test function $\varphi\in (\mathcal S)$, and $y\in \mathcal S'(\mathbb R)$. Define the Gateaux directional derivative of $\varphi$ (in the direction of $y$) by: $$D_y\varphi(x):= …

I have a question regarding the definition of Wick tensor in the framework of the white noise analysis. To put some context to the question we start with the following Gel'fand triple $$S(\mathbb R)\ …

Let $H$ be a Gaussian Hilbert space and $H^{:n:}$ be the homogeneous chaos of order $n$. and let $D_n:=\{(t_1,\cdots,t_n):t_1<t_2<\cdots <t_n\}$. For each $n\geq 0$ there exists an isometry \begin{ali …

Let $W=C_0([0,1],\mathbb R^d)$ be the classical Wiener space equipped with $\mu$ the Wiener measure. If $F:W\to\mathbb R$ is a cylindrical function of the form \begin{align*} F(w)=f(W_{t_1}(w),\cdots, …

I apologize in advance if this question is not suitable for MO (please let me know), but the fact is that since I am not familiar with the theory of Feynman integrals I don't know whether this is a tr …

I am cross-posting this question from MSE since I did not received any answer, furthermore I tried asking some professors in my university but still we could not find an answer. The most surprising th …

Fix $H\in(\frac{1}{2},1)$, and let $\Omega:=C_0([0,T],\mathbb R^d)$ be the space of $\mathbb R^d$-valued continuous functions. There is a probability measure $P^H$ on $(\Omega,\mathcal B(\Omega))$, s …

So the title is quite self explanatory. In the book "Continuous Martingales and Brownian Motion" by Rebuz and Yor, in the proof of Proposition $(2.1)$ of chapter XIII it's stated that: For fixed $t$ …