Integration by parts formulas concerning maxima of some SDEs with applications to study on density functions

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Abstract: In this article, we prove integration by parts (IBP) formulas concerning maxima of solutions to some stochastic differential equations (SDEs). We will deal with three types of maxima. First, we consider discrete time maximum, and then continuous time maximum in the case of one-dimensional SDEs. Finally, we deal with the maximum of the components of a solution to multi-dimensional SDEs. Applications to study their probability density functions by means of the IBP formulas are also discussed.

Original languageEnglish
Pages (from-to)293-317
Number of pages25
JournalStochastic Analysis and Applications
Issue number2
Publication statusPublished - 2016 Mar 3
Externally publishedYes



  • Malliavin calculus
  • maximum process
  • probability density function
  • stochastic differential equation

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

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