Malliavin calculus for non-colliding particle systems

Nobuaki Naganuma, Dai Taguchi

Research output: Contribution to journalArticle

Abstract

In this paper, we use Malliavin calculus to show the existence and continuity of density functions of d-dimensional non-colliding particle systems such as hyperbolic particle systems and Dyson Brownian motion with smooth drift. For this purpose, we apply results proved by Florit and Nualart (1995) and Naganuma (2013) on locally non-degenerate Wiener functionals.

Original languageEnglish
JournalStochastic Processes and their Applications
DOIs
Publication statusAccepted/In press - Jan 1 2019
Externally publishedYes

Fingerprint

Malliavin Calculus
Brownian movement
Particle System
Probability density function
Hyperbolic Systems
Density Function
Brownian motion

Keywords

  • Dyson Brownian motion
  • Hyperbolic particle system
  • Malliavin calculus
  • Non-colliding particle system
  • Non-degeneracy

ASJC Scopus subject areas

  • Statistics and Probability
  • Modelling and Simulation
  • Applied Mathematics

Cite this

Malliavin calculus for non-colliding particle systems. / Naganuma, Nobuaki; Taguchi, Dai.

In: Stochastic Processes and their Applications, 01.01.2019.

Research output: Contribution to journalArticle

@article{6687c1db009045238441057d74a4dc1b,
title = "Malliavin calculus for non-colliding particle systems",
abstract = "In this paper, we use Malliavin calculus to show the existence and continuity of density functions of d-dimensional non-colliding particle systems such as hyperbolic particle systems and Dyson Brownian motion with smooth drift. For this purpose, we apply results proved by Florit and Nualart (1995) and Naganuma (2013) on locally non-degenerate Wiener functionals.",
keywords = "Dyson Brownian motion, Hyperbolic particle system, Malliavin calculus, Non-colliding particle system, Non-degeneracy",
author = "Nobuaki Naganuma and Dai Taguchi",
year = "2019",
month = "1",
day = "1",
doi = "10.1016/j.spa.2019.07.005",
language = "English",
journal = "Stochastic Processes and their Applications",
issn = "0304-4149",
publisher = "Elsevier",

}

TY - JOUR

T1 - Malliavin calculus for non-colliding particle systems

AU - Naganuma, Nobuaki

AU - Taguchi, Dai

PY - 2019/1/1

Y1 - 2019/1/1

N2 - In this paper, we use Malliavin calculus to show the existence and continuity of density functions of d-dimensional non-colliding particle systems such as hyperbolic particle systems and Dyson Brownian motion with smooth drift. For this purpose, we apply results proved by Florit and Nualart (1995) and Naganuma (2013) on locally non-degenerate Wiener functionals.

AB - In this paper, we use Malliavin calculus to show the existence and continuity of density functions of d-dimensional non-colliding particle systems such as hyperbolic particle systems and Dyson Brownian motion with smooth drift. For this purpose, we apply results proved by Florit and Nualart (1995) and Naganuma (2013) on locally non-degenerate Wiener functionals.

KW - Dyson Brownian motion

KW - Hyperbolic particle system

KW - Malliavin calculus

KW - Non-colliding particle system

KW - Non-degeneracy

UR - http://www.scopus.com/inward/record.url?scp=85069689993&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85069689993&partnerID=8YFLogxK

U2 - 10.1016/j.spa.2019.07.005

DO - 10.1016/j.spa.2019.07.005

M3 - Article

AN - SCOPUS:85069689993

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

SN - 0304-4149

ER -