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Invariant distribution of interacting particle system
Fajfrová, Lucie
In the paper we consider interacting particle system that have zero range interactions. It means we have special Markov process with uncountable state space where one state is a configuration of particles on sites and interactions can occur just among particles at the same site. The natural question are invariant measures of this process. We can find some of them and in special cases we can find just set of extremal invariant measures. We deal with a characterization of the invar. measures in some examples.
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Application of S-estimates in robust version of exponential smoothing of times series
Michálek, Jiří
Článek se zabývá využitím tzv. S-odhadů pro robustní vyrovnávání časových řad, které mohou být poškozeny "outliery". Technika S-odhadů je použita pro odhad lokálního koeficientu trendu a lokální úrovně variability. Je odvozena rekurentní formule pro výpočet těchto lokálních charakteristik popisujících chování sledované časové řady. Teoretické výsledky jsou završeny důkazem ekvivariantnosti vůči posunutí u odhadů lokálních parametrů regrese a invariantnosti odhadu úrovně disperze.
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Models of 2D point processes applied to analysis of random sums
Volf, Petr
The contribution deals with the compound (cumulative) random process, i.e. the sequence of random increments at random moments. The process is modeled as a 2D point process (or 2D random counting measure), via the intensities of both components. The study starts from the case of compound Poisson process and generalizes to the cases when the components depend on each other, and also on a set of covariates. An example deals with the sequence of financial transactions.
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