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A stochastic process is a collection of random variables usually indexed by a totally ordered set.

3 votes
1 answer
2k views

first passage time, brownian motion

Hi, If X(t) is Brownian motion in 2D, where X(0) = 0, then we can ask what is the expected time required to first hit a circle of radius R, centered at the origin. This is a First Passage Time prob …
2 votes
0 answers
168 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 ways of …