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Noncolliding Brownian motion (Dyson's Brownian motion model with parameter$\beta=2$) and noncolliding Bessel processes are determinantal processes; thatis, their space-time correlation functions are represented by determinants.Under a proper scaling limit, such as the bulk, soft-edge and hard-edge scalinglimits, these processes converge to determinantal processes describing systemswith an infinite number of particles. The main purpose of this paper is to showthe strong Markov property of these limit processes, which are determinantalprocesses with the extended sine kernel, extended Airy kernel and extendedBessel kernel, respectively. We also determine the quasi-regular Dirichletforms and infinite-dimensional stochastic differential equations associatedwith the determinantal processes.

Strong Markov property of determinantal processes with extended kernels