D. L. Finkelshtein
orcid.org/0000-0001-7136-9399
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Markov dynamics on the cone of discrete Radon measures
Dmitri Finkelshtein, Yuri Kondratiev, Peter Kuchling
MFAT 27 (2021), no. 2, 173-191
173-191
We start with a brief overview of the known facts about the spaces
of discrete Radon measures those may be considered as
generalizations of configuration spaces. Then we study three Markov
dynamics on the spaces of discrete Radon measures: analogues of the
contact model, of the Bolker--Dieckmann--Law--Pacala model, and of
the Glauber-type dynamics. We show how the results obtained
previously for the configuration spaces can be modified for the case
of the spaces of discrete Radon measures.
Стаття розпочинається з короткого огляду відомих фактів про
простори дискретних мір Радона, які можуть розглядатися як
узагальнення просторів конфігурацій. Далі розглядаються три
марківські динаміки на просторах дискретних мір Радона: аналоги
моделі контактів та моделі Болкера--Дікмана--Лоу--Пакали та аналог
динаміки типу Глаубера. Показано як результати, отримані для
просторів конфігурацій, можуть бути узагальнені для випадки
просторів дискретних мір Радона.
Around Ovsyannikov's method
MFAT 21 (2015), no. 2, 134–150
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
D. Finkelshtein, Yu. Kondratiev, O. Kutoviy
MFAT 19 (2013), no. 2, 108-126
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
D. L. Finkelshtein, Yu. G. Kondratiev, M. J. Oliveira
MFAT 18 (2012), no. 1, 55-67
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
MFAT 17 (2011), no. 4, 300-318
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
D. O. Filonenko, D. L. Finkelshtein, Yu. G. Kondratiev
MFAT 14 (2008), no. 3, 209-228
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
D. L. Finkelshtein, Yu. G. Kondratiev
MFAT 11 (2005), no. 2, 126-155
126-155
Spectral gap inequalities on configuration spaces
MFAT 9 (2003), no. 1, 1-8
1-8
Symmetric differential operators of the second order in Poisson spaces
D. L. Finkelshtein, Yu. G. Kondratiev, A. Yu. Konstantinov, M. Röckner
MFAT 6 (2000), no. 4, 14-25
14-25
On exponential model of Poisson spaces
MFAT 4 (1998), no. 4, 5-21
5-21