Hypoelliptic random heat kernels: A case study

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We consider the fundamental solution of a simple hypoelliptic stochastic partial differential equation in which the first-order term is modulated by white noise. We derive some short-time asymptotic formulæ. We discover that the form of the dominant short-time asymptotics depends nontrivially upon the interplay between the geometry of the noisy first-order term and the geometry defined by the hypoelliptic operator.

Original languageEnglish (US)
Pages (from-to)2451-2460
Number of pages10
JournalProceedings of the American Mathematical Society
Issue number8
StatePublished - 2001


  • Fundamental solution
  • Hypoellipticity
  • Stochastic PDE's

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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