Publications

    Published

  1. On exponential model of Poisson spaces (with G. Us)
    Methods of Functional Analysis and Topology, 1998, 4(4), p. 5–21.
  2. Symmetric differential operators of the second order in Poisson spaces (with Yu. Kondratiev, M. Röckner, A. Konstantinov)
    Methods of Functional Analysis and Topology, 2000, 6(4), p. 14–25.
  3. Gauss formula, symmetric extensions of the Laplacian on configuration spaces (with Yu. Kondratiev, M. Röckner, A. Konstantinov),
    Infinite Dimensional Analysis, Quantum Probabilities and Related Topics, 2001, 4(4), p. 489–509.
  4. Spectral gap inequalities on configuration spaces
    Methods of Functional Analysis and Topology, 2003, 9(1), p. 1–8.
  5. Spectral gap inequality on configuration spaces and concentration properties of Poisson measure
    Dopovidi of NASU, 2004, 3, p. 30–36.
  6. Second order differential operators on the configuration spaces
    Proceedings of the Fifth International Conference “Symmetry in Nonlinear Mathematical Physics”, (23–29 June 2003, Kiev, Ukraine), Institute of Mathematics of NASU, Kiev, 2004, Part 3, p. 1301–1307.
  7. Measures on configuration spaces defined by relative energies (with Yu. Kondratiev),
    Methods of Functional Analysis and Topology, 2005, 11(2), p. 126–155.
  8. Equilibrium Glauber dynamics of continuous particle systems as a scaling limit of Kawasaki dynamics (with Yu. Kondratiev, E. Lytvynov)
    Random Operators and Stochastic Equations, 2007, 15(2), p. 105–126.
  9. On two-component contact model in continuum with one independent component (with D. Filonenko, Yu. Kondratiev).
    Methods of Functional Analysis and Topology, 2008, 14(3), p. 209–228.
  10. Measures on two-component configuration spaces,
    Condensed Matter Physics, 2009, 12(1), p. 5–18.
  11. Markov evolutions and hierarchical equations in the continuum I. One-component systems (with Yu. Kondratiev, M. Oliveira).
    Journal of Evolution Equations, 2009, 9(2), p. 197--233.
  12. Individual based model with competition in spatial ecology (with Yu. Kondratiev, O. Kutovyi).
    SIAM Journal on Mathematical Analysis, 2009, 41(1), p. 297--317.
  13. Regulation mechanisms for a free development economic model (with Yu. Kondratiev).
    Journal of Statistical Physics, 2009, 136(1), p. 103–115.
  14. Vlasov scaling for stochastic dynamics of continuous systems (with Yu. Kondratiev, O. Kutovyi).
    Journal of Statistical Physics, 2010, 141(1), p. 158–178.
  15. Binary jumps in continuum. I. Equilibrium processes and their scaling limits (with Yu. Kondratiev, O. Kutovyi, E. Lytvynov).
    Journal of Mathematical Physics, 2011, 52, 063304.
  16. Binary jumps in continuum. II. Non-equilibrium dynamics and their scaling limits (with Yu. Kondratiev, O. Kutovyi, E. Lytvynov).
    Journal of Mathematical Physics, 2011, 52, 113301.
  17. Functional evolutions for homogeneous stationary death-immigration spatial dynamics.
    Methods of Functional Analysis and Topology, 2011, 17(4), p. 300–318.
  18. Vlasov scaling for the Glauber dynamics in continuum (with Yu. Kondratiev, O. Kutovyi).
    Infinite Dimensional Analysis, Quantum Probabilities and Related Topics, 2011, 14(4), p. 537–569.
  19. Semigroup approach to non-equilibrium birth-and-death stochastic dynamics in continuum (with Yu. Kondratiev, O. Kutovyi).
    Journal of Functional Analysis, 2012, 262(3), p. 1274–1308.
  20. An approximative approach to construction of the Glauber dynamics in continuum (with Yu. Kondratiev, O. Kutovyi, E. Zhizhina).
    Mathematische Nachrichten, 2012, 285(2-3), p. 223–235.

    21. Online First

  21. Glauber dynamics in the continuum via generating functionals evolution (with Yu. Kondratiev, M. Oliveira). Complex Analysis and Operator Theory, 2011, doi: 10.1007/s11785-011-0170-1.

    22. To appear

  22. Kawasaki dynamics in the continuum via generating functionals evolution (with Yu. Kondratiev, M. Oliveira).
    1107.4450. To appear in: Methods of Functional Analysis and Topology.
  23. Glauber dynamics in continuum: a constructive approach to evolution of states (with Yu. Kondratiev, Yu. Kozitsky).
    1104.2250. To appear in: Discrete and Continuous Dynamical Systems - Series A.

    24. Submitted

  24. Operator approach to Vlasov scaling for some models of spatial ecology (with Yu. Kondratiev, O. Kutovyi). 1104.2418
  25. Markov evolutions and hierarchical equations in the continuum II. Multicomponent systems (with Yu. Kondratiev, M. J. Oliveira). 1106.4946
  26. Correlation functions evolution for the Glauber dynamics in continuum (with Yu. Kondratiev, O. Kutovyi). 1107.3487
  27. Markovian dynamics in a spacial ecological model with dispersion and competition (with Yu. Kondratiev, Yu. Kozitsky, O. Kutovyi). 1112.0895
  28. Establishment and fecundity in spatial ecological models: functional evolutions (with Yu. Kondratiev, O. Kutovyi). 1112.1973

    29. In preparation

  29. Towards on convolutions on the configuration spaces.
  30. Dynamical self-regulation in spatial population models in continuum (with Yu. Kondratiev).
  31. One- and Two-component Contacts Process with Long Range Interaction in Continuum (with Yu. Kondratiev, A. V. Skorokhod ).
  32. Branching-spreading dynamics in continuum.
  33. Functional evolutions for non-homogeneous non-stationary immigration spatial dynamics.
  34. Vlasov scaling for predator-prey model in continuum (with Yu. Kondratiev, O. Kutovyi).
  35. Equilibrium and non-equilibrium Potts models in continuum (with Yu. Kondratiev, O. Kutovyi).
  36. Split-and-merge systems in continuum (with Yu. Kondratiev, O. Kutovyi).
  37. An ecological model in continuum in bounded region (with Yu. Kondratiev, O. Kutovyi).
  38. From continuous contact model to super-brownian motion (with Yu. Kondratiev, T. Kuna, O. Kutovyi).