3
votes
1answer
61 views

Stable law and Levy distribution

A PDF (probability density function) f(x) is called a stable law if $f(y)=b\int_{-\infty}^{\infty}dx f(by-x)f(x)$ under appropriate values of b. Rewrite this equation in terms of characteristic ...
0
votes
0answers
358 views

Integral of a gaussian with random variance

Assuming: $$X(x,\mu)=\frac{1}{\sqrt{(2\pi)\sigma^2}} \exp[-\frac{1}{2}\frac{(x-\mu)^2}{\sigma^2}]$$ the integral of $X(x,\mu)$ from $-\infty$ to $+\infty$ is: $$S=\int_{-\infty}^{+\infty}dx ...