TY - JOUR
T1 - Strong Markov property of determinantal processes with extended kernels
AU - Osada, Hirofumi
AU - Tanemura, Hideki
N1 - Funding Information:
H.O. is supported in part by a Grant-in-Aid for Scientific Research (KIBAN-A, No. 24244010 ) of the Japan Society for the Promotion of Science . H.T. is supported in part by a Grant-in-Aid for Scientific Research (KIBAN-C, No. 23540122 ) of the Japan Society for the Promotion of Science .
Publisher Copyright:
© 2015 Elsevier B.V. All rights reserved.
PY - 2016/1/1
Y1 - 2016/1/1
N2 - Noncolliding Brownian motion (Dyson's Brownian motion model with parameter β=2) and noncolliding Bessel processes are determinantal processes; that is, their space-time correlation functions are represented by determinants. Under a proper scaling limit, such as the bulk, soft-edge and hard-edge scaling limits, these processes converge to determinantal processes describing systems with an infinite number of particles. The main purpose of this paper is to show the strong Markov property of these limit processes, which are determinantal processes with the extended sine kernel, extended Airy kernel and extended Bessel kernel, respectively. We also determine the quasi-regular Dirichlet forms and infinite-dimensional stochastic differential equations associated with the determinantal processes.
AB - Noncolliding Brownian motion (Dyson's Brownian motion model with parameter β=2) and noncolliding Bessel processes are determinantal processes; that is, their space-time correlation functions are represented by determinants. Under a proper scaling limit, such as the bulk, soft-edge and hard-edge scaling limits, these processes converge to determinantal processes describing systems with an infinite number of particles. The main purpose of this paper is to show the strong Markov property of these limit processes, which are determinantal processes with the extended sine kernel, extended Airy kernel and extended Bessel kernel, respectively. We also determine the quasi-regular Dirichlet forms and infinite-dimensional stochastic differential equations associated with the determinantal processes.
KW - 30C15
KW - 47D07
KW - 60G55
KW - 82C22
KW - MSC 15B52
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U2 - 10.1016/j.spa.2015.08.003
DO - 10.1016/j.spa.2015.08.003
M3 - Article
AN - SCOPUS:84948568461
SN - 0304-4149
VL - 126
SP - 186
EP - 208
JO - Stochastic Processes and their Applications
JF - Stochastic Processes and their Applications
IS - 1
ER -