Displaying similar documents to “Statistical problems on point processes”

Central limit theorem for random measures generated by stationary processes of compact sets

Zbyněk Pawlas (2003)

Kybernetika

Similarity:

Random measures derived from a stationary process of compact subsets of the Euclidean space are introduced and the corresponding central limit theorem is formulated. The result does not require the Poisson assumption on the process. Approximate confidence intervals for the intensity of the corresponding random measure are constructed in the case of fibre processes.

Moments of some random functionals

K. Urbanik (1997)

Colloquium Mathematicum

Similarity:

The paper deals with nonnegative stochastic processes X(t,ω)(t ≤ 0) not identically zero with stationary and independent increments right-continuous sample functions and fulfilling the initial condition X(0,ω)=0. The main aim is to study the moments of the random functionals ∫ 0 ∞ f ( X ( τ , ω ) ) d τ for a wide class of functions f. In particular a characterization of deterministic processes in terms of the exponential moments of these functionals is established.

Moderate deviations for some point measures in geometric probability

Yu Baryshnikov, P. Eichelsbacher, T. Schreiber, J. E. Yukich (2008)

Annales de l'I.H.P. Probabilités et statistiques

Similarity:

Functionals in geometric probability are often expressed as sums of bounded functions exhibiting exponential stabilization. Methods based on cumulant techniques and exponential modifications of measures show that such functionals satisfy moderate deviation principles. This leads to moderate deviation principles and laws of the iterated logarithm for random packing models as well as for statistics associated with germ-grain models and nearest neighbor graphs.

Spatio-temporal modelling of a Cox point process sampled by a curve, filtering and Inference

Blažena Frcalová, Viktor Beneš (2009)

Kybernetika

Similarity:

The paper deals with Cox point processes in time and space with Lévy based driving intensity. Using the generating functional, formulas for theoretical characteristics are available. Because of potential applications in biology a Cox process sampled by a curve is discussed in detail. The filtering of the driving intensity based on observed point process events is developed in space and time for a parametric model with a background driving compound Poisson field delimited by special test...