Integration of brownian vector fields

Yves Le Jan, Olivier Raimond

Research output: Contribution to journalArticlepeer-review

Abstract

Using the Wiener chaos decomposition, we show that strong solutions of non-Lipschitzian stochastic differential equations are given by random Markovian kernels. The example of Sobolev flows is studied in some detail, exhibiting interesting phase transitions.

Original languageEnglish (US)
Pages (from-to)826-873
Number of pages48
JournalAnnals of Probability
Volume30
Issue number2
DOIs
StatePublished - Apr 2002

Keywords

  • Coalescence
  • Dirichlet form
  • Isotropic Brownian flow
  • Stochastic differential equations
  • Stochastic flow
  • Strong solution
  • Wiener chaos decomposition

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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