### 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.

Language | English |
---|---|

Pages | 293-317 |

Number of pages | 25 |

Journal | Stochastic Analysis and Applications |

Volume | 34 |

Issue number | 2 |

DOIs | |

State | Published - 2016 Mar 3 |

Externally published | Yes |

### Fingerprint

### 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

**Integration by parts formulas concerning maxima of some SDEs with applications to study on density functions.** / Nakatsu, Tomonori.

Research output: Contribution to journal › Article

*Stochastic Analysis and Applications*, vol. 34, no. 2, pp. 293-317. DOI: 10.1080/07362994.2015.1129346

}

TY - JOUR

T1 - Integration by parts formulas concerning maxima of some SDEs with applications to study on density functions

AU - Nakatsu,Tomonori

PY - 2016/3/3

Y1 - 2016/3/3

N2 - 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.

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

UR - http://www.scopus.com/inward/record.url?scp=84959100319&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84959100319&partnerID=8YFLogxK

U2 - 10.1080/07362994.2015.1129346

DO - 10.1080/07362994.2015.1129346

M3 - Article

VL - 34

SP - 293

EP - 317

JO - Stochastic Analysis and Applications

T2 - Stochastic Analysis and Applications

JF - Stochastic Analysis and Applications

SN - 0736-2994

IS - 2

ER -