Brownian bridges on Riemannian manifolds |
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| Authors: | Pei Hsu |
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| Institution: | 1. Department of Mathematics, The University of Illinois at Chicago, 322 Science and Engineering Offices, Box 4348, 60680, Chicago, IL, USA
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| Abstract: | We study properties of Brownian bridges on a complete Riemannian manifoldM. LetQ
x,y
t
be the law of Brownian bridge fromx toy with lifetimet. Q
x,y
t
is a probability measure on the space 
x,y
of continuous paths  with (0)=x and (1)=y. We prove thatQ
x,y
t
possesses the large deviation property with the rate function
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![$$J_{x,y} (\omega ) = \frac{1}{2}\left {\int\limits_0^1 {\left| {\dot \omega (s)} \right|^2 ds - \rho (x,y)^2 } } \right].$$](/content/J44TL570T438061H/440_2005_Article_BF01288561_TeX2GIFE1.gif)