Construction of a state evolution for Kawasaki dynamics in continuum

“…Another approach is based on the so-called Ovsyannikov technique and it has been successfully applied in the analysis of birth-and-death as well as hopping particle systems (on a finite time interval), see e.g. [2,3,6].…”

Section: Stochastic Dynamic Equationsmentioning

confidence: 99%

A Survey on Bogoliubov Generating Functionals for Interacting Particle Systems in the Continuum

Finkelshtein

Oliveira

2014

Springer Proceedings in Mathematics &Amp; Statistics

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“…[16], or required more strong assumptions on the birth and death rates (that is less interesting for applications), compare [23] and [8] or [10] and [9]. Moreover, the dynamics with jumps were not covered by the semigroup approach at all, see, e.g., [3,4,14].…”

Section: Introductionmentioning

confidence: 99%

Around Ovsyannikov's method

Finkelshtein

2014

Preprint

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We study existence, uniqueness, and a limiting behaviour of solutions to an abstract linear evolution equation in a scale of Banach spaces. The generator of the equation is a perturbation of the operator which satisfies the classical assumptions of Ovsyannikov's method by a generator of a C0-semigroup acting in each of the spaces of the scale. The results are (slightly modified) abstract version of those considered in [9] for a particular equation. An application to a birth-and-death stochastic dynamics in the continuum is considered.

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“…For a system of particles without interactions such questions were discussed in [30]. The evolution of states as well as mesocopic scaling for the non-equilibrium Kawasaki dynamics in continuum has been thoroughly analyzed in [5] and [6]. The aim of the first part of the present paper is to construct and study the non-equilibrium evolution of states in terms of correlation functions ("statistical" process) corresponding to the generator (1) with transition rates of the following form:…”

mentioning

confidence: 99%

Markov Jump Dynamics with Additive Intensities in Continuum: State Evolution and Mesoscopic Scaling

2015

Self Cite

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We investigate stochastic (conservative) non-equilibrium jump dynamics of interacting particles in continuum. The corresponding evolutions of correlation functions are constructed. The mesoscopic scaling (Vlasov scaling) of the dynamics is studied and the corresponding kinetic equations for the particle densities are derived. Keywords Interacting particle system • Jump dynamics • Non-equilibrium evolution • Vlasov scaling • Kinetic equation 1 Introduction Usually, an infinite group of identical particles with different locations in R d can be characterized by locally finite subset of R d , the points of which are

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Construction of a state evolution for Kawasaki dynamics in continuum

Cited by 6 publications

References 15 publications

A Survey on Bogoliubov Generating Functionals for Interacting Particle Systems in the Continuum

A Survey on Bogoliubov Generating Functionals for Interacting Particle Systems in the Continuum

Around Ovsyannikov's method

Markov Jump Dynamics with Additive Intensities in Continuum: State Evolution and Mesoscopic Scaling

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