# O. V. Kutoviy

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Articles: 3

### Evolution of states and mesoscopic scaling for two-component birth-and-death dynamics in continuum

Methods Funct. Anal. Topology 22 (2016), no. 4, 346-374

Two coupled spatial birth-and-death Markov evolutions on $\mathbb{R}^d$ are obtained as unique weak solutions to the associated Fokker-Planck equations. Such solutions are constructed by its associated sequence of correlation functions satisfying the so-called Ruelle-bound. Using the general scheme of Vlasov scaling we are able to derive a system of non-linear, non-local mesoscopic equations describing the effective density of the particle system. The results are applied to several models of ecology and biology.

### An operator approach to Vlasov scaling for some models of spatial ecology

Methods Funct. Anal. Topology 19 (2013), no. 2, 108-126

We consider Vlasov-type scaling for Markov evolution of birth-and-death 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 non-linear Vlasov-type equation for the density of the limiting system.

### Existence of Gibbs State for Non-Ideal Gas in $R^d$: the case of pair, long-range interaction

Methods Funct. Anal. Topology 10 (2004), no. 3, 33-43