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So the title is quite self-explanatory, suppose we have a stochastic process $(X_t: t\in[0,T])$ where for a fixed $t$, $X_t$ is a $\mathbb R$-valued square integrable random variable, we could even as …

Let $\{L_x(t):(t,x)\in [0,T]\times\mathbb R\}$ be the local time of a Brownian motion $(B_t)_{t\in [0,T]}$, I know that the map $x\mapsto L_x(t)$ is $\alpha$-Hölder for $\alpha<1/2$ (uniformly in time …

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 …

On Zabczyk & Da Prato book about infinite dimensional SDEs they introduce the idea of Gaussian measures in infinite dimensional Banach spaces. They do so by means of Fernique theorem. In the White No …

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 $t$ …