0
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1answer
130 views

Singular distributions: Applications and Instances

Singular distributions are special mathematical objects. They have an interesting property of not having a density function, defined on a set with Lebesgue measure zero. Cantor distribution is the ...
5
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1answer
133 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 ...
1
vote
2answers
280 views

Terrain Generation: Infinite 2D space filled with Diffusion-limited aggregation clusters?

Disclaimer: I don't have a deep understanding of fractals or any higher math, I'm just personally interested in it, so please excuse me if I'm using wrong terms or if I'm being inaccurate. Making ...
3
votes
2answers
294 views

Hausdorff dimension of non-recurrent walks

Preface: I am fairly new to the concept of Hausdorff dimension, so I don't know how interesting a question this is. Identify walks on $\mathbb{Z}$ with infinite binary sequences (say $0$ means moving ...
1
vote
1answer
671 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 ...