Non-explosion of diffusion processes on manifolds with time-dependent metric

Reference : Non-explosion of diffusion processes on manifolds with time-dependent metric


	Document type :	Scientific journals : Article
	Discipline(s) :	Physical, chemical, mathematical & earth Sciences : Mathematics
	To cite this reference:	http://hdl.handle.net/10993/13533

Title :	Non-explosion of diffusion processes on manifolds with time-dependent metric
Language :	English
Author, co-author :	Kuwada, Kazumasa [Ochanomizu University > Department of Mathematics]
	Philipowski, Robert [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Publication date :	2011
Journal title :	Mathematische Zeitschrift
Publisher :	Springer
Volume :	268
Pages :	979-991
Peer reviewed :	Yes
Audience :	International
ISSN :	0025-5874
e-ISSN :	1432-1823
City :	Berlin
Country :	Germany
Keywords :	[en] Ricci flow ; Diffusion process ; Non-explosion ; Radial process
Abstract :	[en] We study the problem of non-explosion of diffusion processes on a manifold with time-dependent Riemannian metric. In particular we obtain that Brownian motion cannot explode in finite time if the metric evolves under backwards Ricci flow. Our result makes it possible to remove the assumption of non-explosion in the pathwise contraction result established by Arnaudon et al. (arXiv:0904.2762, to appear in Sém. Prob.). As an important tool which is of independent interest we derive an Itô formula for the distance from a fixed reference point, generalising a result of Kendall (Ann. Prob. 15:1491–1500, 1987).
Permalink :	http://hdl.handle.net/10993/13533
DOI :	10.1007/s00209-010-0704-7

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