All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 5 Next

Displaying 81 – 100 of 170

Showing per page

Nonlinear filtering in spatio–temporal doubly stochastic point processes driven by OU processes

Michaela Prokešová, Viktor Beneš (2006)

Kybernetika

Doubly stochastic point processes driven by non-Gaussian Ornstein–Uhlenbeck type processes are studied. The problem of nonlinear filtering is investigated. For temporal point processes the characteristic form for the differential generator of the driving process is used to obtain a stochastic differential equation for the conditional distribution. The main result in the spatio-temporal case leads to the filtering equation for the conditional mean.

On an estimation problem for type I censored spatial Poisson processes

Jan Hurt, Petr Lachout, Dietmar Pfeifer (2001)

Kybernetika

In this paper we consider the problem of estimating the intensity of a spatial homogeneous Poisson process if a part of the observations (quadrat counts) is censored. The actual problem has occurred during a court case when one of the authors was a referee for the defense.

On cumulative process model and its statistical analysis

Petr Volf (2000)

Kybernetika

The notion of the counting process is recalled and the idea of the ‘cumulative’ process is presented. While the counting process describes the sequence of events, by the cumulative process we understand a stochastic process which cumulates random increments at random moments. It is described by an intensity of the random (counting) process of these moments and by a distribution of increments. We derive the martingale – compensator decomposition of the process and then we study the estimator of the...

On the conditional intensity of a random measure

Pierre Jacob, Paulo Eduardo Oliveira (1994)

Commentationes Mathematicae Universitatis Carolinae

We prove the existence of the conditional intensity of a random measure that is absolutely continuous with respect to its mean; when there exists an L p -intensity, p > 1 , the conditional intensity is obtained at the same time almost surely and in the mean.

On the strong Brillinger-mixing property of α -determinantal point processes and some applications

Lothar Heinrich (2016)

Applications of Mathematics

First, we derive a representation formula for all cumulant density functions in terms of the non-negative definite kernel function C ( x , y ) defining an α -determinantal point process (DPP). Assuming absolute integrability of the function C 0 ( x ) = C ( o , x ) , we show that a stationary α -DPP with kernel function C 0 ( x ) is “strongly” Brillinger-mixing, implying, among others, that its tail- σ -field is trivial. Second, we use this mixing property to prove rates of normal convergence for shot-noise processes and sketch some applications...

Optimisation in space of measures and optimal design

Ilya Molchanov, Sergei Zuyev (2004)

ESAIM: Probability and Statistics

The paper develops an approach to optimal design problems based on application of abstract optimisation principles in the space of measures. Various design criteria and constraints, such as bounded density, fixed barycentre, fixed variance, etc. are treated in a unified manner providing a universal variant of the Kiefer-Wolfowitz theorem and giving a full spectrum of optimality criteria for particular cases. Incorporating the optimal design problems into conventional optimisation framework makes...

Optimisation in space of measures and optimal design

Ilya Molchanov, Sergei Zuyev (2010)

ESAIM: Probability and Statistics

The paper develops an approach to optimal design problems based on application of abstract optimisation principles in the space of measures. Various design criteria and constraints, such as bounded density, fixed barycentre, fixed variance, etc. are treated in a unified manner providing a universal variant of the Kiefer-Wolfowitz theorem and giving a full spectrum of optimality criteria for particular cases. Incorporating the optimal design problems into conventional optimisation framework...

Perturbing the hexagonal circle packing: a percolation perspective

Itai Benjamini, Alexandre Stauffer (2013)

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

We consider the hexagonal circle packing with radius 1 / 2 and perturb it by letting the circles move as independent Brownian motions for time t . It is shown that, for large enough t , if 𝛱 t is the point process given by the center of the circles at time t , then, as t → ∞ , the critical radius for circles centered at 𝛱 t to contain an infinite component converges to that of continuum percolation (which was shown – based on a Monte Carlo estimate – by Balister, Bollobás and Walters to be strictly bigger than...

Currently displaying 81 – 100 of 170