POISSON PROCESSES FOR SUBSYSTEMS OF FINITE TYPE IN SYMBOLIC DYNAMICS

On the Asymptotic Measure of Periodic Subsystems of Finite Type in Symbolic Dynamics

Let ∆ ( V be a proper subset of the vertices V of the defining graph of an irreducible and aperiodic shift of finite type (Σ+A, T ). Let ∆n be the union of cylinders in Σ + A corresponding to the points x for which the first n-symbols of x belong to ∆ and let μ be an equilibrium state of a Hölder potential φ on Σ+A. We know that μ(∆n) converges to zero as n diverges. We study the asymptotic beh...

Poisson Processes for Susbsystems of Finite Type in Symbolic Dynamical Systems

Let ∆ ( V be a proper subset of the vertices V of the defining graph of an irreducible and aperiodic shift of finite type (Σ A , T ). Let Σ∆ be the subshift of allowable paths in the graph of Σ A which only passes through the vertices of ∆. For a random point x chosen with respect to an equilibrium state μ of a Hölder potential φ on Σ A , let τn be the point process defined as the sum of Dirac ...

Symbolic Dynamics and Finite

Deterministic Thinning of Finite Poisson Processes

Let Π and Γ be homogeneous Poisson point processes on a fixed set of finite volume. We prove a necessary and sufficient condition on the two intensities for the existence of a coupling of Π and Γ such that Γ is a deterministic function of Π, and all points of Γ are points of Π. The condition exhibits a surprising lack of monotonicity. However, in the limit of large intensities, the coupling exi...

Exact Statistical Inference for Some Parametric Nonhomogeneous Poisson Processes

Nonhomogeneous Poisson processes (NHPPs) are often used to model recurrent events, and there is thus a need to check model fit for such models. We study the problem of obtaining exact goodness-of-fit tests for certain parametric NHPPs, using a method based on Monte Carlo simulation conditional on sufficient statistics. A closely related way of obtaining exact confidence intervals in parametri...