Article (Scientific journals)
Non-explosion of diffusion processes on manifolds with time-dependent metric
Kuwada, Kazumasa; PHILIPOWSKI, Robert
2011In Mathematische Zeitschrift, 268, p. 979-991
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Keywords :
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).
Disciplines :
Mathematics
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
Language :
English
Title :
Non-explosion of diffusion processes on manifolds with time-dependent metric
Publication date :
2011
Journal title :
Mathematische Zeitschrift
ISSN :
0025-5874
eISSN :
1432-1823
Publisher :
Springer, Berlin, Germany
Volume :
268
Pages :
979-991
Peer reviewed :
Peer Reviewed verified by ORBi
Available on ORBilu :
since 20 December 2013

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