3
$\begingroup$

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.

Improve this question
$\endgroup$
2
  • 1
    $\begingroup$ What exactly do you mean by "2D Brownian motion, which constitutes a surface"? $\endgroup$
    – j.c.
    Commented Aug 4, 2012 at 16:05
  • $\begingroup$ I wrote it to differentiate it from a 2D BM which has BM in x and y axis which gives us a "line". $\endgroup$
    – id0
    Commented Aug 5, 2012 at 10:57

1 Answer 1

Reset to default
5
$\begingroup$

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).

Improve this answer
$\endgroup$

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .