Victoria Knopova

Senior Research Scientist Institute of Mathematics NAS of Ukraine Kyiv, Ukraine

Research interests

Lévy processes, Lévy-type processes, stochastic differential equations, nonlocal operators, numerical methods for stochastic processes.

Education

2016 Habilitation, Taras Shevchenko National University of Kyiv, Ukraine
2003 PhD in Mathematics
2001–2003 Doctoral student in Mathematics, Swansea University, United Kingdom
2001 MSc in Mathematics
1996–2001 Undergraduate studies in Mathematics, Taras Shevchenko National University of Kyiv

Professional Career

Since 2020–2026 Associate Professor, Taras Shevchenko National University of Kyiv
2017–2020 Teaching and Research Fellow, TU Dresden, Germany
2017 Visiting Lecturer, Wroclaw University, Poland
2009–2017 Visiting Lecturer, Taras Shevchenko National University of Kyiv
2008–2017 Senior Research Fellow, V. M. Glushkov Institute of Cybernetics, NAS of Ukraine
2003–2008 Research Fellow, V. M. Glushkov Institute of Cybernetics, NAS of Ukraine

Grants and Research Visits

Teaching

PhD Supervision

Currently supervising:

Awards

Languages

Ukrainian, Russian (native); English and German (fluent); Polish (basic).

Publications

  1. V. Knopova, Y. Mokanu. On ergodic property of the solution to a Lévy-driven SDE. Kiber. Syst. Anal., 61(5) (2025), 98--109.
  2. D. Ivanenko, V. Knopova, D. Platonov. On Approximation of Some Lévy Processes. Austr. J. Stat., 54(1) (2025), 177--199.
  3. V. Knopova, Y. Mokanu. On Ergodic Properties of Some Levy-Type Processes. J. Theor. Probab., 37(1) (2024), 582--602.
  4. V. Knopova. On recurrence and transience of some Lévy-type processes in ℜ. Theor. Probab. Math. Stat., 108 (2023), 59--75.
  5. V. Knopova, A. Kulik, R. Schilling. Construction and heat kernel estimates of general stable-like Markov processes. Diss. Math., 569 (2021), 1--86.
  6. V. Knopova, Z. Palmowski. Subexponential potential asymptotics with applications. Adv. Appl. Probab., 54(3) (2022), 783--807.
  7. V. Knopova, R. Schilling. Bochner's Subordination and Fractional Caloric Smoothing in Besov and Triebel--Lizorkin Spaces. Math. Nachr., 259(2) (2022), 363--376.
  8. K. Bogdan, V. Knopova, P. Sztonyk. Heat kernel of anisotropic nonlocal operators. Doc. Math., 25 (2020), 1--54.
  9. V. Knopova, A. Kochubei, A. Kulik. Parametrix Methods for Equations with Fractional Laplacians. In: Handbook of Fractional Calculus with Applications, Volume 2, Fractional Differential Equations. A. Kochubei, Yu. Luchko (Eds.), 2019.
  10. V. Knopova, R. Schilling. A Probabilistic proof of the breakdown of Besov regularity in L-shaped domains. In: Stochastic Partial Differential Equations and Related Fields. In Honor of Michael Röckner, SPDERF, Bielefeld, Germany, October 10--14, 2016. Eberle, A., Grothaus, M., Hoh, W., Kassmann, M., Stannat, W., Trutnau, G. (Eds.), 2018, 487--502.
  11. V. Knopova, A. Kulik. Parametrix method and the weak solution to an SDE driven by an α-stable noise. Ann. Inst. Henri Poincaré, 54(1) (2018), 100--140.
  12. V. Knopova, A. Kulik. Intrinsic compound kernel estimates for the transition probability density of a Lévy type processes and their applications. Probab. Math. Stat., 37(1) (2017), 53--100.
  13. Iu. Ganychenko, V. Knopova, A. Kulik. Accuracy of discrete approximation for integral functionals of Markov processes. Modern Stochastics: Theory and Applications, 2(4) (2015), 401--420.
  14. V. Knopova, R. L. Schilling. On level and collision sets of some Feller processes. ALEA: Lat. Am. J. Probab. Math. Stat., 12 (2015), 1001--1029.
  15. V. Knopova. On the Feynman-Kac semigroup for some Markov process. Modern Stoch.: Theory and Appl., 2(2) (2015), 107--129.
  16. V. Knopova, R. Schilling, J. Wang. Lower bounds of the Hausdorff dimension for the images of Feller processes. Stat. Probab. Letters, 97 (2015), 222--228.
  17. V. Knopova, A. Kulik. Parametrix construction for certain Lévy-type processes and applications. Random Oper. Stoch. Eq., 23(2) (2015), 116--136.
  18. V. Knopova, R. Schilling. On the small-time behaviour of Lévy-type processes. Stoch. Proc. Appl., 124(6) (2014), 2249--2265.
  19. V. Knopova. Compound kernel estimates for the transition probability density of a Lévy process in ℝn. Theory of Probab. and Math. Stat., 89 (2014), 57--70.
  20. V. Knopova, A. Kulik. Asymptotic behaviour of the distribution density of the fractional Lévy motion. In: Modern Stochastics and Applications, Springer Series: Optimization and Its Applications, 90 (2013), 175--201.
  21. V. Knopova, A. Kulik. Intrinsic small time estimates for distribution densities of Lévy processes. Random Oper. Stoch. Eq., 21(4) (2013), 321--344.
  22. V. Knopova. On the speed of convergence in the local limit theorem for triangular arrays of random variables. Theory of Stoch. Proc., 18(34), No. 2 (2012), 24--32.
  23. V. Knopova, R. Schilling. A note on the existence of transition probability densities for Lévy processes. Forum Math., 25 (2013), 125--149.
  24. V. Knopova, R. Schilling. Transition density estimates for a class of Lévy and Lévy-type processes. J. Theor. Probab., 25 (2012), 144--170.
  25. N. Jacob, V. Knopova, S. Landwehr, R. Schilling. A geometric interpretation of the transition density of a symmetric Lévy process. Science China: Mathematics, 55 (2012), 1099--1126.
  26. V. Knopova. Asymptotic behaviour of the distribution density of some Lévy functionals in ℝn. Theory Stoch. Proc., 17 (2011), 35--54.
  27. V. Knopova, A. Kulik. Exact asymptotic for distribution densities of Lévy functionals. Electronic J. Probab., 16 (2011), 1394--1433.
  28. V. Knopova. Muckenhoupt-Wheeden theorem for generalized f-Riesz type potentials. Ukr. Math. J., 60(11) (2008), 1520--1528.
  29. V. Knopova, M. Zähle. Spaces of generalized smoothness on h-sets and related Dirichlet forms. Studia Math., 174 (2006), 277--308.
  30. V. Knopova. On a boundary value problem for a pseudo-differential operator and its relation to jump processes. Z. Anal. Anwend., 26(1) (2007), 1--24.
  31. V. Knopova. Continuity of certain pseudo-differential operators in the spaces of generalized smoothness. Ukr. Mat. Zh., 58(5) (2006), 638--652.
  32. N. Jacob, V. Knopova. Fractional derivatives and fractional powers as tools in understanding Wentzel boundary value problems for pseudo-differential operators generating Markov processes. Frac. Calc. Appl. Anal., 8(2) (2005), 91--112.
  33. V. Knopova. Semigroups generated by certain pseudo-differential operators in the half-space ℝn+10+. Coll. Math., 101(4) (2004), 221--235.
  34. V. Knopova. On some operators with complex-valued continuous negative definite symbol which are generators of Lp-sub-Markovian semigroups. Frac. Calc. Appl. Anal., 7(2) (2004), 149--167.
  35. V. Knopova. On a generator of an Lp-sub-Markovian semigroup in ℝn+10+. Random Oper. Stoch. Eq., 12(2) (2004), 185--192.
  36. V. Knopova. Limit behaviour of the renormalized solution to the Airy equation with strongly dependent initial data. Random Oper. Stoch. Eq., 12(1) (2004), 35--42.
  37. V. V. Anh, V. P. Knopova, N. N. Leonenko. Continuous-time stochastic processes with cyclical long-range dependence. Austr. New Zealand Stat. J., 46(2) (2004), 275--296.
  38. N. Leonenko, V. Knopova. Limiting behaviour of the rescaled solution to the Airy equation with random strongly dependent initial conditions. Dopovidi NAN Ukr., 9 (2002), 47--50.
  39. V. Knopova, T. Pepelyaeva. On some stochastic models of financial mathematics. Cybernet. System. Anal., 37(3--4) (2001), 427--433.
  40. L. Beghin, V. Knopova, N. Leonenko, E. Orsingher. Gaussian limiting behaviour of the rescaled solution to the linear Korteweg--de Vries equation with random initial conditions. J. Statist. Phys., 99 (2000), 769--781.