TY - JOUR
T1 - Malliavin calculus for non-colliding particle systems
AU - Naganuma, Nobuaki
AU - Taguchi, Dai
N1 - Funding Information:
The authors thank Professor Ryo Takada of Kyushu University for his valuable suggestion and an anonymous referee for his/hervaluable comments that led to improve our manuscript. This work was supported by JSPS KAKENHI Grant Numbers JP17K14202 and JP17H06833 .
Publisher Copyright:
© 2019 Elsevier B.V.
PY - 2020/4
Y1 - 2020/4
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
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U2 - 10.1016/j.spa.2019.07.005
DO - 10.1016/j.spa.2019.07.005
M3 - Article
AN - SCOPUS:85069689993
SN - 0304-4149
VL - 130
SP - 2384
EP - 2406
JO - Stochastic Processes and their Applications
JF - Stochastic Processes and their Applications
IS - 4
ER -