Vlasov scaling for stochastic dynamics of continuous systems
arXiv:1002.4698 · doi:10.1007/s10955-010-0038-1
Abstract
We describe a general scheme of derivation of the Vlasov-type 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 the realization of the proposed approach in particular models are presented.
23 pages
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- On an aggregation in birth-and-death stochastic dynamics
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- Non-equilibrium dynamics for a Widom-Rowlinson type model with mutations
- Dynamical Widom-Rowlinson model and its mesoscopic limit
- Binary jumps in continuum. II. Non-equilibrium process and a Vlasov-type scaling limit
- Spatial growth processes with long range dispersion: microscopics, mesoscopics, and discrepancy in spread rate
- Vlasov scaling for the Glauber dynamics in continuum
- Evolution of states and mesoscopic scaling for two-component birth-and-death dynamics in continuum
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- Fractional statistical dynamics and fractional kinetics
- Asymptotic Behavior of the Subordinated Traveling Waves
- Fractional kinetic hierarchies and intermittency