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

Tomonori Nakatsu

doi:10.1080/07362994.2015.1129346

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

Tomonori Nakatsu

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

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 language	English
Pages (from-to)	293-317
Number of pages	25
Journal	Stochastic Analysis and Applications
Volume	34
Issue number	2
DOIs	https://doi.org/10.1080/07362994.2015.1129346
Publication status	Published - 2016 Mar 3
Externally published	Yes

Keywords

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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10.1080/07362994.2015.1129346

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AB - 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.

KW - Malliavin calculus

KW - maximum process

KW - probability density function

KW - stochastic differential equation

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

Abstract

Keywords

ASJC Scopus subject areas

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