# D. L. Finkelshtein

orcid.org/0000-0001-7136-9399
Search this author in Google Scholar

Articles: 9

### Around Ovsyannikov's method

Dmitri 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 [10] for a particular equation. An application to a birth-and-death stochastic dynamics in the continuum is considered.

### 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.

### Kawasaki dynamics in the continuum via generating functionals evolution

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.

### Functional evolutions for homogeneous stationary death-immigration spatial dynamics

D. Finkelshtein

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.

### On two-component contact model in continuum with one independent component

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.

### Measures on configuration spaces defined by relative energies

Methods Funct. Anal. Topology 11 (2005), no. 2, 126-155

### Spectral gap inequalities on configuration spaces

D. L. Finkelshtein

Methods Funct. Anal. Topology 9 (2003), no. 1, 1-8

### Symmetric differential operators of the second order in Poisson spaces

Methods Funct. Anal. Topology 6 (2000), no. 4, 14-25

### On exponential model of Poisson spaces

Methods Funct. Anal. Topology 4 (1998), no. 4, 5-21