Curriculum Vitae

Кнопова В.П.

Особиста інформація

Кнопова Вікторія Павлівна

✈ Кафедра теорії ймовірностей, статистики та актуарної математики,        Київський національний університет імені Тараса Шевченка,        Володимирська, 64, Київ, 01601 Україна ☎ +38 044 431-04-67 | ✉ vicknopova@knu.ua Громадянство: Україна Аккаунт (профіль) в наукометричних базах даних: | ORCID | Scopus | Google Scholar | Zentralblatt MATH | Володіння мовами: українська, російська, англійська, німецька

Область досліджень і наукові інтереси:

• Псевдо-диференціальні оператори і пов`язані з ними марковські процеси
• Процеси Леві
• Моделювання випадкових процесів

Ґранти:

• Dresden Senior Fellowship (2014)
• DFG Fellowship (2004-2005б 2013-2015)
• INTAS Young Scientist Fellowship (2007-2008)
• DAAD Fellowship (2009)
• Грант Президента України для молодих вчених (2007-2008)

Нагороди, премії:

• Премія Верховної Ради України (2011)
• Премія Президента України для молодих вчених (2018)

Конференції, семінари, воркшопи

• Науковий семінар 'Мехматівські читання', Україна, Київ (2025)
  Назва доповіді: (Log)-Sobolev inequality from the stochastic perspective
• KyivAcademUs 2025, 7-9.05. 2025 , Україна, Київ (2025)
  Назва доповіді: Процеси Маркова та інтегро-диференціальні рівняння
• Modern Stochastics: Theory and Applications VI, Україна, Київ (2025)
  Назва доповіді: On "stochastic" functional inequalities
• SPA2025, Wroclaw (2025)
  Назва доповіді: On dynamic approximation scheme for Levy processes
• Он-лайн Семінар "Malliavin Calculus and its Applications", Україна, Київ (2024)
  Назва доповіді: Parametrix technique for a Levy-type model with unbounded coefficients
• One-Parameter Semigroups of Operators 2024: Stochastics & Dynamics, Laval (Canada) (online) (2024)
  Назва доповіді: Simulation of Levy (type) processes: dynamic approximation
• Науковий семінар 'Мехматівські читання", Київ, Україна (2024)
  Назва доповіді: Нелокальні диференціальні рівняння та процеси Маркова
• Nonlocal Operators and Markov Processes, Poland, Bedlewo (2023)
  Назва доповіді: Paramtrix construction for a Levy-type operator with unbounded jump kernel
• Probabilistic and game theoretical interpretation of PDEs, Мадрид, Іспанія (2023)
  Назва доповіді: On some non-local operators and related Levy-type processes
• Georgian Mathematical Union XII Annual International Conference, Batumi, Georgia (2022)
• Probability and Analysis 2022, Wroclaw, Poland (2022)
• Int. Conf. “Modern Stochastics: Theory and Applications V”, Kiev, Ukraine (2021)
• Pseudo-Differential Operators and Markov Processes. Marking 40 Years of Contributions to Mathematics by Professor Niels Jacob , Swansea, UK (2021)
• Joint meeting of the Italian Mathematical Union, the Italian Society of Industrial and Applied Mathematics and the Polish Mathematical Society, Wroclaw, Poland (2018)
• Semigroups of Operators: Theory and Applications, Kazimierz Dolny, Poland (2018)
• Probability and Analysis, Bedlewo, Poland (2015)
• Probability, reliability and optimization, Kyiv, Ukraine (2015)
• Stochastic Processes in Abstract Spaces, dedicated to the 80th anniversary of Professor A.Ya. Dorogovtsev., Kyiv, Ukraine (2015)
• 7-th International Conference of Analysis and its applications, Seoul, South Korea (2014)
• International Congress of Mathematicians, Seoul, South Korea (2014)

Публікації

• Підручники і навчальні посібники

• В. Кнопова, Б.Манікін "Моделювання випадкових процесів". он-лайн, 120 p. - 2026
• В. Кнопова "Вступ до багатовимірної статистики". Vol.00 (он-лайн матеріал, бета версія), 141 p. - 2024

• Статті

• 2025
• D. Ivanenko, V. Knopova, D. Platonov "On Approximation of Some Lévy Processes". Austrian Journal of Statistics , Vol.54, Iss.1 pp. 177 - 199, - 2025
• V. Knopova, Y. Mokanu. "On ergodic property of the solution to a Lévy-driven SDE". Kiber. Syst.Anal., Vol.61, Iss.5 pp. 98 - 109, - 2025
• 2024
• V. Knopova, Y. Mokanu "On Ergodic Properties of Some Levy-Type Processes". Journal of Theoretical Probability , Vol.37, Iss.1 pp. 582 - 602, - 2024
• 2023
• V. Knopova "On recurrence and transience of some Lévy-type processes in R". Theor. Probability and Math. Statist. DOI: https://doi.org/10.1090/tpms/1187, Vol.108, pp. 59 - 75, - 2023
• 2022
• V. Knopova, R. Schilling "Bochner`s subordination and Fractional Caloric Smoothing in Besov and Triebel-Lizorkin Spaces". Math. Nachr., Vol.259, Iss.2 pp. 363 - 376, - 2022
• V. Knopova, Z. Palmowski "Subexponential potential asymptotics with applications". Adv. Appl. Probab., Vol.54, Iss.3 pp. 783 - 807, - 2022
• 2021
• V. Knopova, A. Kulik, R. Schilling "Construction and heat kernel estimates of general stable-like Markov processes". Dissertationes Mathematicae, Vol.569, pp. 1 - 86, - 2021
• 2020
• K. Bogdan, V. Knopova, P. Sztonyk. "Heat kernel of anisotropic nonlocal operators". Documenta Mathematicae, Vol.25, pp. 1 - 54, - 2020
• 2019
• V. Knopova, A. Kochubei, A. Kulik "Parametrix Methods for Equations with Fractional Laplacians". Section in: Fractional Differential Equations, Vol.2, pp. 267 - 299, - 2019
• 2018
• V. Knopova, A. Kulik "The parametrix method and the weak solution to an SDE driven by an $alpha$-stable noise". Annales Inst. Henri Poincaré, Vol.54, Iss.1 pp. 100 - 140, - 2018
• V. Knopova, R. Schilling "A Probabilistic proof of the breakdown of Besov regularity in L-shaped domains.". Stochastic Partial Differential Equations and Related Fields. Special Issue In Honor of Michael Roeckner., pp. 487 - 502, - 2018
• 2017
• V. Knopova, A. Kulik. "Intrinsic compound kernel estimates for the transition probability density of a Lévy-type process and their applications. ". Probab. Math. Stat. , Vol.37, Iss.1 pp. 53 - 100, - 2017
• 2015
• Iu. Ganychenko, V. Knopova, A. Kulik. "Accuracy of discrete approximation for integral functionals of Markov processes". Modern Stochastics: Theory and Applications, Vol.2, Iss.4 pp. 401 - 420, - 2015
• V. Knopova, A. Kulik. "Parametrix construction for certain Lévy-type processes and applications. ". Rand. Oper. Stoch. Eq., Vol.23, Iss.2 pp. 116 - 136, - 2015
• V. Knopova, R. Schilling, J. Wang " Lower bounds of the Hausdorff dimension for the images of Feller processes". Stat. Probab. Letters., Vol.97, pp. 222 - 228, - 2015
• V. Knopova, R. Schilling " On level and collision sets of some Feller processes". Lat. Am. J. Probab. Math. Stat., Vol.12, pp. 1001 - 1029, - 2015
• V. Knopova " On the Feynman-Kac semigroup for some Markov process". Modern Stoch.: Theory and Appl., Vol.2, Iss.2 pp. 107 - 129, - 2015
• 2014
• V. Knopova. " Compound kernel estimates for the transition probability density of a Lévy process in R^n.". Theory of Probab. and Math. Stat., Vol.89, pp. 57 - 70, - 2014
• V. Knopova, R. Schilling. "On the small-time behaviour of Lévy-type processes. ". Stoch. Proc. Appl. , Vol.124, pp. 2249 - 2265, - 2014
• V. Knopova, A. Kulik "Asymptotiv behaviour of the distribution density of the fractional Lévy motion.". Proceedings of the MSTA-3 Conference volume, Modern StochasticsandApplications, Springer series: Optimization and Its Applications, Vol.90, pp. 175 - 201, - 2014
• 2013
• V. Knopova, R.Schilling "A note on the existence of transition probability densities for Lévy processes. ". Forum Math. , Vol.25, pp. 125 - 149, - 2013
• V. Knopova, A. Kulik. "Intrinsic small time estimates for distribution densities of Lévy processes. ". Random Oper. Stoch. Eqs. , Vol.21, Iss.4 pp. 321 - 344, - 2013
• 2012
• V. Knopova "On the speed of convergence in the local limit theorem for triangular arrays of random variables.". Theory of Stoch. Proc. , Vol.18 (34, Iss.2 pp. 24 - 32, - 2012
• V. Knopova, R.Schilling "Transition Density Estimates for a Class of Lévy and Lévy-Type Processes". J. Theor. Probab., Vol.25, pp. 144 - 170, - 2012
• N.Jacob, V. Knopova, S.Landwehr, R.Schilling "A geometric interpretation of the transition density of a symmetric Lévy process". Science China: Mathematics., Vol.55, Iss.6 pp. 1099 - 1126, - 2012
• 2011
• V. Knopova. "Asymptotic behaviour of the distribution density of some Lévy functionals in R^n.". Theory Stoch. Proc. 17 , pp. 35 - 54, - 2011
• V. Knopova, A. Kulik "Exact asymptotic for distribution densities of Lévy functionals". Electr. J. Probab. , Vol.16, pp. 1394 - 1433, - 2011
• 2008
• V. Knopova "Muckenhoupt-Wheeden theorem for generalized f-Riesz type potentials". Ukr. Math. J. Vol. 60, No. 11, pp. 1520 - 1528, - 2008
• 2007
• V. Knopova "On a boundary value problem for a pseudo-differential operator and its relation to jump processes". Z. Anal. Anwend., Vol. 26, Issue 1, pp. 1 - 24, - 2007
• 2006
• V. Knopova. " Continuity of certain pseudo-differential operators in the spaces of generalized smoothness. ". Ukr. Mat. Zh. 58 (5) , pp. 638 - 652, - 2006
• V. Knopova, M. Zaehle "Spaces of generalized smoothness on h-sets and related Dirichlet forms". Stud. Math. 174, No. 3, pp. 277 - 308, - 2006
• 2005
• 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) , pp. 91 - 112, - 2005
• 2004
• 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) , pp. 275 - 296, - 2004
• V. Knopova. "Limit behaviour of the renormalized solution to the Airy equation with strongly dependent initial data. ". Ran. Oper. Stoch. Eq. 12 (1), pp. 35 - 42, - 2004
• V. Knopova. "On a generator of an L_p -sub-Markovian semigroup in R^{n+1}_{0+}. ". Ran. Oper. Stoch. Eq. 12 (2) , pp. 185 - 192, - 2004
• V. Knopova. "Semigroups generated by certain pseudo-differential operators in the half- space R^{n+1}_{0+} . ". Coll. Math. 101 (4) , pp. 221 - 235, - 2004
• V. Knopova. " On some operators with complex-valued continuous negative definite symbol which are generators of L p -sub-Markovian semigroups. ". Frac. Calc. Appl. Anal. 7 (2), pp. 149 - 167, - 2004
• 2002
• N. Leonenko, V. Knopova. " Limiting behaviour of the rescaled solution to the Airy equation with random strongly dependent initial conditions.". Dopowidi NAN Ukr. 9 , pp. 47 - 50, - 2002
• 2001
• V. Knopova, T. Pepelyaeva. "On some stochastic models of financial mathematics. ". Cybern. System. Anal. 37 (3-4) , pp. 427 - 433, - 2001
• 2000
• 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. 9 (3-4) , pp. 769 - 781, - 2000