D. L. Finkelshtein
Methods Funct. Anal. Topology 21 (2015), no. 2, 134–150
We study existence, uniqueness, and a limiting behavior 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 $C_0$-semigroup acting in each of the spaces of the scale. The results are (slightly modified) abstract version of those considered in  for a particular equation. An application to a birth-and-death stochastic dynamics in the continuum is considered.
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.
Methods Funct. Anal. Topology 18 (2012), no. 1, 55-67
We construct the time evolution of Kawasaki dynamics for a spatial infinite particle system in terms of generating functionals. This is carried out by an Ovsjannikov-type result in a scale of Banach spaces, which leads to a local (in time) solution. An application of this approach to Vlasov-type scaling in terms of generating functionals is considered as well.
Methods Funct. Anal. Topology 17 (2011), no. 4, 300-318
We discover death-immigration non-equilibrium stochastic dynamics in the continuum also known as the Surgailis process. Explicit expression for the correlation functions is presented. Dynamics of states and their generating functionals are studied. Ergodic properties for the evolutions are considered.
Methods Funct. Anal. Topology 14 (2008), no. 3, 209-228
Properties of a contact process in continuum for a system of particles of two types, one which is independent of the other, are considered. We study dynamics of the first and the second order correlation functions, their asymptotics, and the dependence on parameters of the~system.
Methods Funct. Anal. Topology 11 (2005), no. 2, 126-155
Methods Funct. Anal. Topology 9 (2003), no. 1, 1-8
Methods Funct. Anal. Topology 6 (2000), no. 4, 14-25
Methods Funct. Anal. Topology 4 (1998), no. 4, 5-21