Date: 19 Apr 2011

Stochastically Incomplete Manifolds and Graphs

* Final gross prices may vary according to local VAT.

Get Access


We survey geometric properties which imply the stochastic incompleteness of the minimal diffusion process associated to the Laplacian on manifolds and graphs. In particular, we completely characterize stochastic incompleteness for spherically symmetric graphs and show that, in contrast to the case of Riemannian manifolds, there exist examples of stochastically incomplete graphs of polynomial volume growth.

Mathematics Subject Classification (2000). Primary 39A12; Secondary 58J65.