On the mean first arrival time of Brownian particles on Riemannian manifolds

Medet Nursultanov, Justin C. Tzou, Leo Tzou

Research output: Contribution to journalArticlepeer-review

Abstract

We use geometric microlocal methods to compute an asymptotic expansion of mean first arrival time for Brownian particles on Riemannian manifolds. This approach provides a robust way to treat this problem, which has thus far been limited to very special geometries. This paper can be seen as the Riemannian 3-manifold version of the planar result of [1] and thus enable us to see the full effect of the local extrinsic boundary geometry on the mean arrival time of the Brownian particles. Our approach also connects this question to some of the recent progress on boundary rigidity and integral geometry [21] and [18].

Original languageEnglish
Pages (from-to)202-240
Number of pages39
JournalJournal des Mathematiques Pures et Appliquees
Volume150
DOIs
Publication statusPublished - Jun 2021

Keywords

  • Narrow escape problem
  • Mean sojourn time
  • Brownian motion

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