Relationship With Brownian Motion
The stochastic process Xt given by
(where Wt is a standard Brownian motion and ) is a Brownian motion with drift ν.
Then, the first passage time for a fixed level by Xt is distributed according to an inverse-gaussian:
Read more about this topic: Inverse Gaussian Distribution
Famous quotes containing the words relationship with, relationship and/or motion:
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—Mary Pipher (20th century)
“Every relationship that does not raise us up pulls us down, and vice versa; this is why men usually sink down somewhat when they take wives while women are usually somewhat raised up. Overly spiritual men require marriage every bit as much as they resist it as bitter medicine.”
—Friedrich Nietzsche (1844–1900)
“till disproportion’d sin
Jarr’d against natures chime, and with harsh din
Broke the fair musick that all creatures made
To their great Lord, whose love their motion sway’d
In perfect Diapason, whilst they stood
In first obedience, and their state of good.”
—John Milton (1608–1674)