# Yu. G. Kondratiev

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### Fractional kinetics in a spatial ecology model

José Luís da Silva, Yuri Kondratiev, Pasha Tkachov

Methods Funct. Anal. Topology **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

Methods Funct. Anal. Topology **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

Methods Funct. Anal. Topology **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

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

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

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.

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

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

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

D. L. Finkelshtein, Yu. G. Kondratiev

Methods Funct. Anal. Topology **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

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

### Correlation functionals for Gibbs measures and Ruelle bounds

Yuri G. Kondratiev, Tobias Kuna

Methods Funct. Anal. Topology **9** (2003), no. 1, 9-58

### Analytic aspects of Poissonian white noise analysis

Yuri G. Kondratiev, Tobias Kuna, Maria João Oliveira

Methods Funct. Anal. Topology **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

Methods Funct. Anal. Topology **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

Methods Funct. Anal. Topology **5** (1999), no. 4, 87-100

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

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

Methods Funct. Anal. Topology **5** (1999), no. 1, 29-64

### Marked Gibbs measures via cluster expansion

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

Methods Funct. Anal. Topology **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

Methods Funct. Anal. Topology **4** (1998), no. 2, 1-15

### Differential geometry on compound Poisson space

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

Methods Funct. Anal. Topology **4** (1998), no. 1, 32-58

### Generalized Appell systems

Yuri G. Kondratiev, José Luis Silva, Ludwig Streit

Methods Funct. Anal. Topology **3** (1997), no. 3, 28-61

### Complex Gaussian analysis and the Bargman-Segal space

Martin Grothaus, Yuri G. Kondratiev, Ludwig Streit

Methods Funct. Anal. Topology **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

Methods Funct. Anal. Topology **3** (1997), no. 1, 62-81

### Quantum hierarchical model

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

Methods Funct. Anal. Topology **2** (1996), no. 3, 1-35

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

Yu. M. Berezansky, Yu. G. Kondratiev

Methods Funct. Anal. Topology **2** (1996), no. 2, 1-50

### Dirichlet operators semigroups in some Gibbs lattice spin systems

S. Albeverio, A. Val. Antoniouk, A. Vict. Antoniouk, Yu. G. Kondratiev

Methods Funct. Anal. Topology **1** (1995), no. 1, 3-27