Point Processes with Papangelou Conditional Intensity: From the Skorohod Integral to the Dirichlet Form

G.L. Torrisi

2013, v.19, Issue 2, 195-248

ABSTRACT

We provide the Dirichlet form associated to a point process with Papangelou conditional intensity on a Riemannian manifold, computeits generator and prove existence and uniqueness of the corresponding diffusion. Moreover, we give a diffusion approximation, at the level of the Dirichlet form, by Kawasaki dynamics in continuum. Our approach relies on some sample path relations among the Skorohod integral and the gradients. The results are valid under quite general conditions and are potentially applicable to various classes of point processes. By way of example, we apply the theory to Poisson processes, and classes of finite and infinite pairwise interaction point processes with weakly differentiable pair interaction function.

Keywords: Diffusion approximation,diffusion process,Dirichlet form,Gibbsprocess,Kawasaki dynamics in continuum,pairwise interaction point process,Point process,Poisson proces

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