Publications

    Published

  1. Accelerated nonlocal nonsymmetric dispersion for monostable equations on the real line. (with P. Tkachov). Applicable Analysis, 2017, doi: 10.1080/00036811.2017.1400537, (25 pages).
  2. Global stability in a nonlocal reaction-diffusion equation. (with Yu. Kondratiev, S. Molchanov, P. Tkachov). Stochastic and Dynamics, 2018, 18 (5), 1850037 (15 pages).
  3. Around Ovsyannikov's method. Methods of Functional Analysis and Topology, 2015, 21 (2), p. 134–150.
  4. Dynamical Widom-Rowlinson model and its mesoscopic limit (with Yu. Kondratiev, O. Kutovyi, M. J. Oliveira). Journal of Statistical Physics, 2015, 158 (1), p. 57–86.
  5. The statistical dynamics of a spatial logistic model and the related kinetic equation (with Yu. Kondratiev, Yu. Kozitsky, O. Kutovyi). Mathematical Models and Methods in Applied Sciences, 2015, 25 (2), p. 343–370.
  6. Density behavior of spatial birth-and-death stochastic evolution of mutating genotypes under selection rates (with Yu. Kondratiev, O. Kutovyi, S. Molchanov, E. Zhizhina). Russian Journal of Mathematical Physics, 2014, 21 (4), p. 450–459.
  7. Statistical dynamics of continuous systems: perturbative and approximative approaches (with Yu. Kondratiev, O. Kutovyi). Arabian Journal of Mathematics, 2014, (electronic) doi:10.1007/s40065-014-0111-8.
  8. A survey on Bogoliubov generating functionals for interacting particle systems in the continuum (with M. J. Oliveira). In: From Particle Systems to Partial Differential Equations, ed. by C. Bernardin and P. Gonçalves. Springer Proceedings in Mathematics & Statistics, 75. Springer-Verlag Berlin Heidelberg, 2014, p. 161–177.
  9. On an aggregation in birth-and-death stochastic dynamics (with Yu. Kondratiev, O. Kutovyi, E. Zhizhina). Nonlinearity, 2014, 27, p. 1105–1133.
  10. A mathematical framework for the analysis of spatial-temporal point processes (with O. Ovaskainen, O. Kutovyi, S. Cornell, B. Bolker, Yu. Kondratiev). Theoretical Ecology, 2014, 7(1), p. 101–113.
  11. Establishment and fecundity in spatial ecological models: statistical approach and kinetic equations (with Yu. Kondratiev, O. Kutovyi). Infinite Dimensional Analysis, Quantum Probabilities and Related Topics, 2013, 16(2), 1350014 (24 pages).
  12. An operator approach to Vlasov scaling for some models of spatial ecology (with Yu. Kondratiev, O. Kutovyi). Methods of Functional Analysis and Topology, 2013, 19(2), p. 108–126.
  13. Markov evolutions and hierarchical equations in the continuum II. Multicomponent systems (with Yu. Kondratiev, M. J. Oliveira). Reports on Mathematical Physics, 2013, 71(1), p. 123–148.
  14. Stochastic evolution of a continuum particle system with dispersal and competition: Micro- and mesoscopic description (with Yu. Kondratiev, Yu. Kozitsky, O. Kutovyi) The European Physical Journal Special Topics, 2013, 216(1), p. 107–116.
  15. Glauber dynamics in continuum: a constructive approach to evolution of states (with Yu. Kondratiev, Yu. Kozitsky). Discrete and Continuous Dynamical Systems - Series A, 2013, 33(4), p. 1431–1450.
  16. On convolutions on configuration spaces. II. Spaces of locally finite configurations. Ukrainian Mathematical Journal, 2013, 64(12), p. 1919–1944.
  17. On convolutions on configuration spaces. I. Spaces of finite configurations. Ukrainian Mathematical Journal, 2013, 64(11), p. 1752–1775.
  18. Correlation functions evolution for the Glauber dynamics in continuum (with Yu. Kondratiev, O. Kutovyi). Semigroup Forum, 2012, 85, p. 289–306.
  19. Glauber dynamics in the continuum via generating functionals evolution (with Yu. Kondratiev, M. Oliveira). Complex Analysis and Operator Theory, 2012, 6(4), p. 923–945.
  20. Kawasaki dynamics in the continuum via generating functionals evolution(with Yu. Kondratiev, M. Oliveira).
    Methods of Functional Analysis and Topology, 2012, 18(1), p. 55–67.
  21. 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.
  22. Semigroup approach to birth-and-death stochastic dynamics in continuum (with Yu. Kondratiev, O. Kutovyi).
    Journal of Functional Analysis, 2012, 262(3), p. 1274–1308.
  23. 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.
  24. Functional evolutions for homogeneous stationary death-immigration spatial dynamics.
    Methods of Functional Analysis and Topology, 2011, 17(4), p. 300–318.
  25. 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.
  26. 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.
  27. Vlasov scaling for stochastic dynamics of continuous systems (with Yu. Kondratiev, O. Kutovyi).
    Journal of Statistical Physics, 2010, 141(1), p. 158–178.
  28. Regulation Mechanisms in Spatial Stochastic Development Models (with Yu. Kondratiev).
    Journal of Statistical Physics, 2009, 136(1), p. 103–115.
  29. Individual based model with competition in spatial ecology (with Yu. Kondratiev, O. Kutovyi).
    SIAM Journal on Mathematical Analysis, 2009, 41(1), p. 297--317.
  30. 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.
  31. Measures on two-component configuration spaces,
    Condensed Matter Physics, 2009, 12(1), p. 5–18.
  32. 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.
  33. 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.
  34. Measures on configuration spaces defined by relative energies (with Yu. Kondratiev),
    Methods of Functional Analysis and Topology, 2005, 11(2), p. 126–155.
  35. 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.
  36. Spectral gap inequality on configuration spaces and concentration properties of Poisson measure
    Dopovidi of NASU, 2004, 3, p. 30–36.
  37. Spectral gap inequalities on configuration spaces
    Methods of Functional Analysis and Topology, 2003, 9(1), p. 1–8.
  38. 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.
  39. 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.
  40. On exponential model of Poisson spaces (with G. Us)
    Methods of Functional Analysis and Topology, 1998, 4(4), p. 5–21.

    41. In preparation

  41. Markov evolution of continuum particle systems with dispersion and competition (with Yu. Kondratiev, Yu. Kozitsky, O. Kutovyi).
  42. Self-aggregation in Markov evolution with density dependent death and branching in the continuum (with Yu. Kondratiev, O. Kutovyi, E. Zhizhina).
  43. A family of equivalent mesoscopic scalings for continuous particle systems (with Yu. Kondratiev, O. Kutovyi, E. Lytvynov).
  44. A cooking book for spatio-temporal point process models in theoretical ecology (with O. Ovaskainen, O. Kutovyi, S. Cornell, B. Bolker, Yu. Kondratiev).
  45. Dynamical self-regulation in spatial population models in continuum (with Yu. Kondratiev).
  46. One- and Two-component Contacts Process with Long Range Interaction in Continuum (with Yu. Kondratiev, A. V. Skorokhod ).
  47. Branching-spreading dynamics in the continuum.
  48. Functional evolutions for non-homogeneous non-stationary immigration spatial dynamics.
  49. Vlasov scaling for predator-prey model in the continuum (with Yu. Kondratiev, O. Kutovyi).
  50. Split-and-merge systems in continuum (with Yu. Kondratiev, O. Kutovyi).
  51. An ecological model in continuum in bounded region (with Yu. Kondratiev, O. Kutovyi).
  52. From continuous contact model to super-brownian motion (with Yu. Kondratiev, T. Kuna, O. Kutovyi).