Results 1  10
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30
INDIVIDUAL BASED MODEL WITH COMPETITION IN SPATIAL ECOLOGY
, 2008
"... We analyze an interacting particle system with a Markov evolution of birthanddeath type. We have shown that a local competition mechanism (realized via a density dependent mortality) leads to a globally regular behavior of the population in course of the stochastic evolution. ..."
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Cited by 17 (9 self)
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We analyze an interacting particle system with a Markov evolution of birthanddeath type. We have shown that a local competition mechanism (realized via a density dependent mortality) leads to a globally regular behavior of the population in course of the stochastic evolution.
Operator approach to Vlasov scaling for some models of spatial ecology
 IN PREPARATION
, 2013
"... We consider Vlasovtype scaling for Markov evolution of birthanddeath type in continuum, which is based on a proper scaling of corresponding Markov generators and has an algorithmic realization in terms of related hierarchical chains of correlation functions equations. The existence of rescaled a ..."
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Cited by 7 (5 self)
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We consider Vlasovtype scaling for Markov evolution of birthanddeath type in continuum, which is based on a proper scaling of corresponding Markov generators and has an algorithmic realization in terms of related hierarchical chains of correlation functions equations. The existence of rescaled and limiting evolutions of correlation functions and convergence to the limiting evolution are shown. The obtained results enable us to derive a nonlinear Vlasovtype equation for the density of the limiting system.
Vlasov scaling for stochastic dynamics of continuous systems
, 2010
"... We describe a general derivation scheme for the Vlasovtype equations for Markov evolutions of particle systems in continuum. This scheme is based on a proper scaling of corresponding Markov generators and has an algorithmic realization in terms of related hierarchical chains of correlation functio ..."
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Cited by 6 (6 self)
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We describe a general derivation scheme for the Vlasovtype equations for Markov evolutions of particle systems in continuum. This scheme is based on a proper scaling of corresponding Markov generators and has an algorithmic realization in terms of related hierarchical chains of correlation functions equations. Several examples of realization of the proposed approach in particular models are presented.
Kawasaki dynamics in continuum: micro and mesoscopic descriptions
, 2011
"... The time evolution of an infinite system of interacting point particles on Rd is described on both micro and mesoscopic levels as the evolution µ0 7 → µt of probability measures on the configuration space Γ. The particles are supposed to hop over Rd and repel each other, similarly to the Kawasaki ..."
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Cited by 6 (1 self)
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The time evolution of an infinite system of interacting point particles on Rd is described on both micro and mesoscopic levels as the evolution µ0 7 → µt of probability measures on the configuration space Γ. The particles are supposed to hop over Rd and repel each other, similarly to the Kawasaki dynamics on the lattice Zd. The microscopic description is based on solving linear equations for the correlation functions by means of a combination of methods including an Ovcyannikovtype technique, which yields the evolution in a scale of Banach spaces. Then the evolution of the corresponding measures is obtained therefrom by a special procedure based on local approximations. The mesoscopic description is performed within the Vlasov scaling method, which yields a linear infinite chain of equations obtained from those for the correlation function of the model. Its main peculiarity is that for the initial r0 being the correlation function of the inhomogeneous Poisson measure with density %0, the solution rt is the correlation function of such a measure with density %t which solves a nonlinear differential equation of convolution type. 1
Correlation functions evolution for the Glauber dynamics in continuum
, 2012
"... We construct a correlation functions evolution corresponding to the Glauber dynamics in continuum. Existence of the corresponding strongly continuous contraction semigroup in a proper Banach space is shown. Additionally we prove the existence of the evolution of states and study their ergodic proper ..."
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Cited by 5 (5 self)
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We construct a correlation functions evolution corresponding to the Glauber dynamics in continuum. Existence of the corresponding strongly continuous contraction semigroup in a proper Banach space is shown. Additionally we prove the existence of the evolution of states and study their ergodic properties.
An approximative approach to construction of the Glauber dynamics in continuum
, 2011
"... We develop a new approach for the construction of the Glauber dynamics in continuum. Existence of the corresponding strongly continuous contraction semigroup in a proper Banach space is shown. Additionally we present the finite and infinitevolume approximations of the semigroup by families of bou ..."
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Cited by 5 (5 self)
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We develop a new approach for the construction of the Glauber dynamics in continuum. Existence of the corresponding strongly continuous contraction semigroup in a proper Banach space is shown. Additionally we present the finite and infinitevolume approximations of the semigroup by families of bounded linear operators.
Glauber Dynamics in Continuum: A Constructive Approach to Evolution of States∗
"... The evolutions of states is described corresponding to the Glauber dynamics of an infinite system of interacting particles in continuum. The description is conducted on both micro and mesoscopic levels. The microscopic description is based on solving linear equations for correlation functions by ..."
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Cited by 5 (5 self)
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The evolutions of states is described corresponding to the Glauber dynamics of an infinite system of interacting particles in continuum. The description is conducted on both micro and mesoscopic levels. The microscopic description is based on solving linear equations for correlation functions by means of an Ovsjannikovtype technique, which yields the evolution in a scale of Banach spaces. The mesoscopic description is performed by means of the Vlasov scaling, which yields a linear infinite chain of equations obtained from those for the correlation function. Its main peculiarity is that, for the initial correlation function of the inhomogeneous Poisson measure, the solution is the correlation function of such a measure with density which solves a nonlinear differential equation of convolution type. 1
Metric properties of discrete time exclusion type processes in continuum
, 2009
"... A new class of exclusion type processes acting in continuum with synchronous updating is introduced and studied. Ergodic averages of particle velocities are obtained and their connections to other statistical quantities, in particular to the particle density (the so called Fundamental Diagram) is an ..."
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Cited by 4 (2 self)
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A new class of exclusion type processes acting in continuum with synchronous updating is introduced and studied. Ergodic averages of particle velocities are obtained and their connections to other statistical quantities, in particular to the particle density (the so called Fundamental Diagram) is analyzed rigorously. The main technical tool is a “dynamical” coupling applied in a nonstandard fashion: we do not prove the existence of the successful coupling (which even might not hold) but instead use its presence/absence as an important diagnostic tool. Despite that this approach cannot be applied to lattice systems directly, it allows to obtain new results for the lattice systems embedding them to the systems in continuum. Applications to the traffic flows modelling are discussed as well. 1