Yu. G. Kondratiev

Search this author in Google Scholar

Articles: 28

Diffusion approximation for transport equations with dissipative drifts

Luca Di Persio, Yuri Kondratiev, Viktorya Vardanyan

↓ Abstract   |   Article (.pdf)

MFAT 28 (2022), no. 1, 1-11


We study stochastic differential equations with a small perturbation parameter. Under the dissipative condition on the drift coefficient and the local Lipschitz condition on the drift and diffusion coefficients we prove the existence and uniqueness result for the perturbed SDE, also the convergence result for the solution of the perturbed system to the solution of the unperturbed system when the perturbation parameter approaches zero. We consider the application of the above-mentioned results to the Cauchy problem and the transport equations.

Вивчаються стохастичні диференціальні рівняння з невеликим параметр збурення. За умови дисипативності коефіцієнту дрейфа у випадку, коли дрейф та коефіцієнти дифузії задовольняють локальній умови Ліпшица, доведено існування та єдиність розв'язку збуреного стохастичного диференціального рівняння. Також отримано результат про збіжність розв'язку збуреної системи до розв'язку незбуреної системи у разі коли параметр збурення прямує до нуля. Розглянуто застосування вищезазначених результатів до задачі Коші та рівняння транспорту.

Green Measures for Time Changed Markov Processes

Yuri Kondratiev, José Luís da Silva

↓ Abstract   |   Article (.pdf)

MFAT 27 (2021), no. 3, 227-236


In this paper we study Green measures for certain classes of random time change Markov processes where the random time change are inverse subordinators. We show the existence of the Green measure for these processes under the condition of the existence of the Green measure of the original Markov processes and they coincide. Applications to fractional dynamics in given.

У цій роботі досліджуються міри Гріна для деяких класів марківських процесів з випадковою заміною часу, де випадкова заміна часу є оберненим субординатором. Показано існування міри Гріна для цих процесів за умови існування міри Гріна вихідних марківських процесів і що вони збігаються. Також даються застосування отриманих результатів до динаміки процесів із дробовими похідними.

Markov dynamics on the cone of discrete Radon measures

Dmitri Finkelshtein, Yuri Kondratiev, Peter Kuchling

↓ Abstract   |   Article (.pdf)

MFAT 27 (2021), no. 2, 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.

Representations of the Infinite-Dimensional Affine Group

Yuri Kondratiev

↓ Abstract   |   Article (.pdf)

MFAT 26 (2020), no. 4, 348-355


We introduce an infinite-dimensional affine group and construct its irreducible unitary representation. Our approach follows the one used by Vershik, Gelfand and Graev for the diffeomorphism group, but with modifications made necessary by the fact that the group does not act on the phase space. However it is possible to define its action on some classes of functions.

Вводиться нескінченновимірна аффінна група і будується її незвідне унітарне представлення. Наш підхід наслідує метод Вершика-Гельфанда-Граєва для групи дифеоморфізмів, з необхідними модифікаціями, пов’язаними з тим, що група не діє на фазовому просторі, але можна визначити її дію на деяких класах функцій.

Green measures for Markov processes

Yuri Kondratiev, José L. da Silva

↓ Abstract   |   Article (.pdf)

MFAT 26 (2020), no. 3, 241-248


In this paper we study Green measures of certain classes of Markov processes. In particular Brownian motion and processes with jump generators with different tails. The Green measures are represented as a sum of a singular and a regular part given in terms of the jump generator. The main technical question is to find a bound for the regular part.

Ми вивчаємо міри Ґріна для деяких класів марківських процесів. Зокрема для броунівського руху і стрибкових процесів. Міри Ґріна містять сингулярну і регулярну компоненти. Основна задача полягає в оцінці регулярної частини.

Weak-coupling limit for ergodic environments

Martin Friesen, Yuri Kondratiev

↓ Abstract   |   Article (.pdf)

MFAT 25 (2019), no. 2, 118-133


The main aim of this work is to establish an averaging principle for a wide class of interacting particle systems in the continuum. This principle is an important step in the analysis of Markov evolutions and is usually applied for the associated semigroups related to backward Kolmogorov equations, c.f. [27]. Our approach is based on the study of forward Kolmogorov equations (a.k.a. Fokker-Planck equations). We describe a system evolving as a Markov process on the space of finite configurations, whereas its rates depend on the actual state of another (equilibrium) process on the space of locally finite configurations. We will show that ergodicity of the environment process implies the averaging principle for the solutions of the coupled Fokker-Planck equations.

Automorphisms generated by umbral calculus on a nuclear space of entire test functions

Ferdinand Jamil, Yuri Kondratiev, Sheila Menchavez, Ludwig Streit

↓ Abstract   |   Article (.pdf)

MFAT 24 (2018), no. 4, 339-348


In this paper we show that Sheffer operators, mapping monomials to certain Sheffer polynomial sequences, such as falling and rising factorials, Charlier, and Hermite polynomials extend to continuous automorphisms on the space of entire functions of first order growth and minimal type.

Fractional kinetics in a spatial ecology model

José Luís da Silva, Yuri Kondratiev, Pasha Tkachov

↓ Abstract   |   Article (.pdf)

MFAT 24 (2018), no. 3, 275-287


In this paper we study the effect of subordination to the solution of a model of spatial ecology in terms of the evolution density. The asymptotic behavior of the subordinated solution for different rates of spatial propagation is studied. The difference between subordinated solutions to non-linear equations with classical time derivative and solutions to non-linear equation with fractional time derivative is discussed.

Fractional statistical dynamics and fractional kinetics

José Luís da Silva, Anatoly N. Kochubei, Yuri Kondratiev

↓ Abstract   |   Article (.pdf)

MFAT 22 (2016), no. 3, 197-209


We apply the subordination principle to construct kinetic fractional statistical dynamics in the continuum in terms of solutions to Vlasov-type hierarchies. As a by-product we obtain the evolution of the density of particles in the fractional kinetics in terms of a non-linear Vlasov-type kinetic equation. As an application we study the intermittency of the fractional mesoscopic dynamics.

Fractional contact model in the continuum

Anatoly N. Kochubei, Yuri G. Kondratiev

↓ Abstract   |   Article (.pdf)

MFAT 21 (2015), no. 2, 179–187


We consider the evolution of correlation functions in a non-Markov version of the contact model in the continuum. The memory effects are introduced by assuming the fractional evolution equation for the statistical dynamics. This leads to a behavior of time-dependent correlation functions, essentially different from the one known for the standard contact model.

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

D. Finkelshtein, Yu. Kondratiev, O. Kutoviy

↓ Abstract   |   Article (.pdf)

MFAT 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

D. L. Finkelshtein, Yu. G. Kondratiev, M. J. Oliveira

↓ Abstract   |   Article (.pdf)

MFAT 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.

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

D. O. Filonenko, D. L. Finkelshtein, Yu. G. Kondratiev

↓ Abstract   |   Article (.pdf)

MFAT 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

D. L. Finkelshtein, Yu. G. Kondratiev

MFAT 11 (2005), no. 2, 126-155


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

Yu. G. Kondratiev, O. V. Kutoviy, E. A. Pechersky

MFAT 10 (2004), no. 3, 33-43


Correlation functionals for Gibbs measures and Ruelle bounds

Yuri G. Kondratiev, Tobias Kuna

MFAT 9 (2003), no. 1, 9-58


Analytic aspects of Poissonian white noise analysis

Yuri G. Kondratiev, Tobias Kuna, Maria João Oliveira

MFAT 8 (2002), no. 4, 15-48


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


On a spectral representation for correlation measures in configuration space analysis

Yuri M. Berezansky, Yuri G. Kondratiev, Tobias Kuna, Eugene Lytvynov

MFAT 5 (1999), no. 4, 87-100


Analysis and geometry on ${\mathbb R}_{+}$-marked configuration space

Yuri G. Kondratiev, Eugene W. Lytvynov, Georgi F. Us

MFAT 5 (1999), no. 1, 29-64


Marked Gibbs measures via cluster expansion

Jose L. Da Silva, Yuri G. Kondratiev, Tobias Kuna

MFAT 4 (1998), no. 4, 50-81


Some examples of Dirichlet operators associated with the actions of infinite dimensional Lie groups

S. Albeverio, A. Daletskii, Yu. Kondratiev

MFAT 4 (1998), no. 2, 1-15


Differential geometry on compound Poisson space

Yuri G. Kondratiev, José L. Silva, Ludwig Streit

MFAT 4 (1998), no. 1, 32-58


Generalized Appell systems

Yuri G. Kondratiev, José Luis Silva, Ludwig Streit

MFAT 3 (1997), no. 3, 28-61


Complex Gaussian analysis and the Bargman-Segal space

Martin Grothaus, Yuri G. Kondratiev, Ludwig Streit

MFAT 3 (1997), no. 2, 46-64


Euclidean Gibbs states for quantum continuous systems with Boltzmann statistics via cluster expansion

Yu. G. Kondratiev, A. L. Rebenko, M. Röckner, M. Röckner, G. V. Shchepanʹuk

MFAT 3 (1997), no. 1, 62-81


Quantum hierarchical model

S. Albeverio, Yu. G. Kondratiev, Yu. V. Kozitsky

MFAT 2 (1996), no. 3, 1-35


Biorthogonal systems in hypergroups: an extension of non-Gaussian analysis

Yu. M. Berezansky, Yu. G. Kondratiev

MFAT 2 (1996), no. 2, 1-50


All Issues