Displaying similar documents to “On asymptotic cyclicity of doubly stochastic operators”

Asymptotic behaviour in the set of nonhomogeneous chains of stochastic operators

Małgorzata Pułka (2012)

Discussiones Mathematicae Probability and Statistics

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We study different types of asymptotic behaviour in the set of (infinite dimensional) nonhomogeneous chains of stochastic operators acting on L¹(μ) spaces. In order to examine its structure we consider different norm and strong operator topologies. To describe the nature of the set of nonhomogeneous chains of Markov operators with a particular limit behaviour we use the category theorem of Baire. We show that the geometric structure of the set of those stochastic operators which have...

Stochastic differential equation driven by a pure-birth process

Marta Tyran-Kamińska (2002)

Annales Polonici Mathematici

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A generalization of the Poisson driven stochastic differential equation is considered. A sufficient condition for asymptotic stability of a discrete time-nonhomogeneous Markov process is proved.

Applications of the Kantorovich-Rubinstein maximum principle in the theory of Markov semigroups

Henryk Gacki

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We present new sufficient conditions for the asymptotic stability of Markov operators acting on the space of signed measures. Our results are based on two principles. The first one is the LaSalle invariance principle used in the theory of dynamical systems. The second is related to the Kantorovich-Rubinstein theorems concerning the properties of probability metrics. These criteria are applied to stochastically perturbed dynamical systems, a Poisson driven stochastic differential equation...

Dynamics and density evolution in piecewise deterministic growth processes

Michael C. Mackey, Marta Tyran-Kamińska (2008)

Annales Polonici Mathematici

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A new sufficient condition is proved for the existence of stochastic semigroups generated by the sum of two unbounded operators. It is applied to one-dimensional piecewise deterministic Markov processes, where we also discuss the existence of a unique stationary density and give sufficient conditions for asymptotic stability.

Stochastic vortices in periodically reclassified populations

Gracinda Rita Guerreiro, João Tiago Mexia (2008)

Discussiones Mathematicae Probability and Statistics

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Our paper considers open populations with arrivals and departures whose elements are subject to periodic reclassifications. These populations will be divided into a finite number of sub-populations. Assuming that: a) entries, reclassifications and departures occur at the beginning of the time units; b) elements are reallocated at equally spaced times; c) numbers of new elements entering at the beginning of the time units are...

Fast simulation for Road Traffic Network

Roberta Jungblut-Hessel, Brigitte Plateau, William J. Stewart, Bernard Ycart (2010)

RAIRO - Operations Research

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In this paper we present a method to perform fast simulation of large Markovian systems. This method is based on the use of three concepts: Markov chain uniformization, event-driven dynamics, and modularity. An application of urban traffic simulation is presented to illustrate the performance of our approach.

On uniformly smoothing stochastic operators

Wojciech Bartoszek (1995)

Commentationes Mathematicae Universitatis Carolinae

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We show that a stochastic operator acting on the Banach lattice L 1 ( m ) of all m -integrable functions on ( X , 𝒜 ) is quasi-compact if and only if it is uniformly smoothing (see the definition below).