Reference : Non-explosion of diffusion processes on manifolds with time-dependent metric
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/13533
Non-explosion of diffusion processes on manifolds with time-dependent metric
English
Kuwada, Kazumasa mailto [Ochanomizu University > Department of Mathematics]
Philipowski, Robert mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
2011
Mathematische Zeitschrift
Springer
268
979-991
Yes
International
0025-5874
1432-1823
Berlin
Germany
[en] Ricci flow ; Diffusion process ; Non-explosion ; Radial process
[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).
http://hdl.handle.net/10993/13533
10.1007/s00209-010-0704-7

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