arXiv 1007.18932010-07math.PRmath-phmath.MP

相对论性扩散的非爆炸判据

Nonexplosion criteria for relativistic diffusions

Ismaël Bailleul, Jacques Franchi

备注：: Published in at http://dx.doi.org/10.1214/11-AOP672 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)
发表信息：: Annals of Probability 2012, Vol. 40, No. 5, 2168-2196
DOI：: 10.1214/11-AOP672

摘要：

一些广义洛伦兹协变算子，与所谓的Θ（或θ）-相对论扩散相关，在任何洛伦兹流形中都有意义，已经由Franchi和Le Jan [Comm. Pure Appl. Math. 60（2007）187-251]，Franchi和Le Jan [Curvature diffusions in general relativity（2010）.未出版的手稿）。到目前为止，只研究了几个例子。在这项工作中，我们提供了一些非爆炸的标准，这些扩散，可用于一般情况下。

英文摘要：

Some general Lorentz covariant operators, associated to the so-called Θ(or Ξ)-relativistic diffusions and making sense in any Lorentzian manifold, have been introduced by Franchi and Le Jan [Comm. Pure Appl. Math. 60 (2007) 187-251], Franchi and Le Jan [Curvature diffusions in general relativity (2010). Unpublished manuscript]. Only a few examples have been studied so far. We provide in this work some nonexplosion criteria for these diffusions, which can be used in generic cases.

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