On minimal parabolic functions and time-homogeneous parabolic <IMG ALIGN=BOTTOM HEIGHT=14 WIDTH=10>-transforms期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

按检索

On minimal parabolic functions and time-homogeneous parabolic -transforms

Authors:	Krzysztof Burdzy Thomas S Salisbury

Institution:	Department of Mathematics, Box 354350, University of Washington, Seattle, Washington 98195-4350 ; Department of Mathematics and Statistics, York University, Toronto, Ontario, Canada M3J 1P3

Abstract:	Does a minimal harmonic function remain minimal when it is viewed as a parabolic function? The question is answered for a class of long thin semi-infinite tubes $D\subset \mathbb{R}^{d}$ of variable width and minimal harmonic functions corresponding to the boundary point of ``at infinity.' Suppose is the width of the tube units away from its endpoint and is a Lipschitz function. The answer to the question is affirmative if and only if $\int ^{\infty }f^{3}(u)du = \infty$ . If the test fails, there exist parabolic -transforms of space-time Brownian motion in with infinite lifetime which are not time-homogenous.

Keywords:	Martin boundary harmonic functions parabolic functions Brownian motion $h$-transforms

	点击此处可从《Transactions of the American Mathematical Society》浏览原始摘要信息
	点击此处可从《Transactions of the American Mathematical Society》下载免费的PDF全文