On density functions related to discrete time maximum of some one-dimensional diffusion processes

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Abstract

This article focuses on the probability density functions related to the discrete time maximum of some one-dimensional diffusion processes. Firstly, we shall consider solutions of one-dimensional stochastic differential equations and prove an integration by parts formula on the discrete time maximum of the solutions. The smoothness, expressions and upper bounds of the density function will be obtained by the formula. Secondly, Gaussian processes will be dealt with. For some Gaussian processes, we shall obtain asymptotic behaviors of the density functions related to the discrete time maximum of the processes. The Malliavin calculus and Laplace's method play important roles for the proofs.

Original languageEnglish
Article number127672
JournalApplied Mathematics and Computation
Volume441
DOIs
Publication statusPublished - 2023 Mar 15

Keywords

  • Asymptotic behavior
  • Diffusion process
  • Discrete time maximum
  • Laplace's method
  • Malliavin calculus
  • Probability density function

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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