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

Kazumasa Kuwada, Robert Philipowski

Research output: Contribution to journalArticlepeer-review

20 Citations (Scopus)

Abstract

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).

Original languageEnglish
Pages (from-to)979-991
Number of pages13
JournalMathematische Zeitschrift
Volume268
Issue number3-4
DOIs
Publication statusPublished - 2011 Aug 1

Keywords

  • Diffusion process
  • Non-explosion
  • Radial process
  • Ricci flow

ASJC Scopus subject areas

  • Mathematics(all)

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