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

Henryk Gacki

  • 2007

Abstract

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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 and a mathematical model of the cell cycle. Moreover, we discuss the problem of the asymptotic stability of solutions of a generalized version of the Tjon-Wu equation.

How to cite

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Henryk Gacki. Applications of the Kantorovich-Rubinstein maximum principle in the theory of Markov semigroups. 2007. <http://eudml.org/doc/286029>.

@book{HenrykGacki2007,
abstract = {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 and a mathematical model of the cell cycle. Moreover, we discuss the problem of the asymptotic stability of solutions of a generalized version of the Tjon-Wu equation.},
author = {Henryk Gacki},
keywords = {asymptotic stability; Markov operators; Fortet-Mourier metric; Hutchinson metric; invariance principle; stochastic differential equation},
language = {eng},
title = {Applications of the Kantorovich-Rubinstein maximum principle in the theory of Markov semigroups},
url = {http://eudml.org/doc/286029},
year = {2007},
}

TY - BOOK
AU - Henryk Gacki
TI - Applications of the Kantorovich-Rubinstein maximum principle in the theory of Markov semigroups
PY - 2007
AB - 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 and a mathematical model of the cell cycle. Moreover, we discuss the problem of the asymptotic stability of solutions of a generalized version of the Tjon-Wu equation.
LA - eng
KW - asymptotic stability; Markov operators; Fortet-Mourier metric; Hutchinson metric; invariance principle; stochastic differential equation
UR - http://eudml.org/doc/286029
ER -

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