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Topic: zeros of heat-extensions, Brownian motion
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Posts: 11
Registered: 10/24/08
zeros of heat-extensions, Brownian motion
Posted: May 26, 2011 8:00 AM
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Hi, if I take an nontrivial L^2 function f on R^n, its heat extension
F in R^{n+1}_+ is real analytic on each plane and nonzero almost
everywhere. (correct?)

1. How bad can its zero set be?

In particular,

2. Let Z be Brownian motion in R^n x [0,oo), started at (0, T). Can I
say that the process F(Z_t) is almost surely non-zero for all t>0?
(till Z hits boundary). Or is that F(Z_t) is non-zero for all t>0,
almost surely?



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