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

Tomonori Nakatsu

Applied Mathematics and Computation, 2023, vol. 441, issue C

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.

Keywords: Diffusion process; Discrete time maximum; Probability density function; Malliavin calculus; Asymptotic behavior; Laplace’s method (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:441:y:2023:i:c:s0096300322007408

DOI: 10.1016/j.amc.2022.127672

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