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Hi

I know about the Brownian bridge, for example $B_t = W_t - tW(1)$. Is it possible to create it in 2D? ie, to have a 2D Brownian motion, which constitutes a surface, and have it return to 0 when the distance (according to some metric) from the center is equal to some constant?

For example, to have an image which is a Brownian motion realization and have it conditioned as equal to 0 on the unit circle.

Thanks.

flag	asked Aug 4 at 11:29 id0 31●3

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What exactly do you mean by "2D Brownian motion, which constitutes a surface"? – jc Aug 4 at 16:05

I wrote it to differentiate it from a 2D BM which has BM in x and y axis which gives us a "line". – id0 Aug 5 at 10:57

Steve Huntsman · Answer 1 · 2012-08-04 14:43:42Z UTC

3

A natural generalization of the Brownian bridge that should be readily adaptable to your problem is furnished by a Gaussian free field (see in particular the picture on the wiki page).

answered Aug 4 at 14:43

Steve Huntsman
8,139●1●22●56

Brownian bridge in two variables?

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