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

Research output: Contribution to journalArticle

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 293-317 25 Stochastic Analysis and Applications 34 2 https://doi.org/10.1080/07362994.2015.1129346 Published - 2016 Mar 3 Yes

### Fingerprint

Probability density function
Differential equations
Stochastic differential equations
Density function

### Keywords

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

### ASJC Scopus subject areas

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

### Cite this

In: Stochastic Analysis and Applications, Vol. 34, No. 2, 03.03.2016, p. 293-317.

Research output: Contribution to journalArticle

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