0
votes
1answer
29 views

Canonical Separation of variables

Do the functions of the form $\psi(x)\phi(y)$ span $L^2(\mathbf{R}^6)$? Insert proper grammar here.
1
vote
1answer
107 views

An integral evaluation

I tried my luck with Wolfram Alpha, with $p \in \mathbb{R}$ $$\int_{-\infty}^{\infty} \frac{x^p}{1+x^2} dx = \frac{1}{2} \pi ((-1)^p+1) \sec(\frac{\pi p}{2})$$ for $-1<p<1$, and doesn't exist ...
2
votes
1answer
329 views

Derivatives of Brownian motion or Box Options Greeks

Here's the probability (I think) that a particle in Brownian motion (w/ standard deviation $\sqrt{t}$) will exceed $m$ between times $t_1$ and $t_2$: $$\frac1{2\sqrt{2\pi}}\int_{-\infty }^m ...