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	Limit theorem for derivative martingale at criticality w.r.t branching Brownian motion
	Yang, Ting ; Ren, Yan-Xia
	2011
关键词	Branching Brownian motion Derivative martingale Spine construction Traveling wave solution K-P-P equation
英文摘要	We consider a branching Brownian motion on R in which one particle splits into 1 + X children. There exists a critical value (lambda) under bar in the sense that (lambda) under bar is the lowest velocity such that a traveling wave solution to the corresponding Kolmogorov-Petrovskii-Piskunov equation exists. It is also known that the traveling wave solution with velocity (lambda) under bar is closely connected with the rescaled Laplace transform of the limit of the so-called derivative martingale partial derivative W-t((lambda) under bar). Thus special interest is put on the property of its limit partial derivative W((lambda) under bar. Kyprianou [Kyprianou, A.E., 2004. Traveling wave solutions to the K-P-P equation: alternatives to Simon Harris' probability analysis. Ann. Inst. H. Poincare 40,53-72.] proved that, partial derivative W((lambda) under bar) > 0 if EX(log(+) X)(2+delta) < +infinity for some delta > 0 while partial derivative W ((lambda) under bar) = 0 if EX (log(+) X)(2-delta) = +infinity. It is conjectured that partial derivative W((lambda) under bar is non-degenerate if and only if EX (log(+) X)(2) < +infinity. The purpose of this article is to prove this conjecture. (C) 2010 Elsevier B.V. All rights reserved.; http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000287109500004&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=8e1609b174ce4e31116a60747a720701 ; Statistics & Probability; SCI(E); 5; ARTICLE; 2; 195-200; 81
语种	英语
出处	SCI
出版者	statistics probability letters
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/157658]
专题	数学科学学院
推荐引用方式 GB/T 7714	Yang, Ting,Ren, Yan-Xia. Limit theorem for derivative martingale at criticality w.r.t branching Brownian motion. 2011-01-01.

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