5
votes
1answer
139 views

Escape Time of Fractional Brownian Motion

Let $B(t)$ be Brownian motion with $B(0)=x>0$ and let $A>x$. It is well known that the expected time for $B(t)$ to escape the interval $[0,A]$ is equal to $x(A-x)$. Is the expected time known ...
2
votes
0answers
153 views

A fractal object at origin but nowhere else: derived from Brownain motion

Hi, Please consider this object: Start with a realization of Brownian motion in 2D, which I'll denote by rho(t) where -infinity < t < +infinity. Next, lets smooth rho. There are various ...
1
vote
2answers
323 views

Fractional Gaussian noise in higher dimensions

I'm having difficulty imagining (or explaining to myself) how the partial sums a two dimensional Gaussian noise can produce a surface. According to equation (20) of the paper, "On two-dimensional ...
1
vote
1answer
680 views

Need help understanding Mandelbrot and Van Ness Fractional Brownian Motion

I need help understanding the Mandelbot and Van Ness' definition of Fractional Brownian motion $ B_H( t , \omega ) - B_H( 0 , \omega ) = \frac{1}{\Gamma(H + \frac{1}{2})} \left\( \int_{-\infty}^0 ...