Victoria Knopova

• Pseudo-differential operators and related Markov processes
  
• Lévy processes
  
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• Past courses:
  
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• Tutorials: Probability I, Statistics, Discrete Mathematics.
  
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• Special courses: Lévy processes, Stochastic Analysis, Limit theorems for stochastic processes, SDE I, SDE II.
  

• DFG Fellowship
  
• INTAS Young Scientist Fellowship
  
• DAAD Fellowship
  
• Grant of President of Ukraine for young scientists
  

Conferences

• Nonlocal Operators and Markov Processes, Poland, Bedlewo (2023)
  Title of the talk: Invited talk.
• 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)

Publications

Articles

2023
• V. Knopova, Y. Mokanu "On Ergodic Properties of Some Levy-Type Processes". Journal of Theoretical Probability (online version, DOI 10.1007/s10959-023-01252-x), pp. 1 - 21, - 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, Iss. pp. 1 - 86, - 2021
2020
• K. Bogdan, V. Knopova, P. Sztonyk. "Heat kernel of anisotropic nonlocal operators". Documenta Mathematicae, Vol.25, Iss. 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, Iss. 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
• 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, Iss. pp. 222 - 228, - 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
• 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, R. Schilling " On level and collision sets of some Feller processes". Lat. Am. J. Probab. Math. Stat., Vol.12, Iss. pp. 1001 - 1029, - 2015
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, Iss. pp. 175 - 201, - 2014
• V. Knopova, R. Schilling. "On the small-time behaviour of Lévy-type processes. ". Stoch. Proc. Appl. , Vol.124, Iss. pp. 2249 - 2265, - 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, Iss.0 pp. 57 - 70, - 2014
2013
• V. Knopova, R.Schilling "A note on the existence of transition probability densities for Lévy processes. ". Forum Math. , Vol.25, Iss.0 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
• 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
• V. Knopova, R.Schilling "Transition Density Estimates for a Class of Lévy and Lévy-Type Processes". J. Theor. Probab., Vol.25, Iss. pp. 144 - 170, - 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
2011
• V. Knopova, A. Kulik "Exact asymptotic for distribution densities of Lévy functionals". Electr. J. Probab. , Vol.16, Iss. pp. 1394 - 1433, - 2011
• V. Knopova. "Asymptotic behaviour of the distribution density of some Lévy functionals in R^n.". Theory Stoch. Proc. 17 , pp. 35 - 54, - 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, M. Zaehle "Spaces of generalized smoothness on h-sets and related Dirichlet forms". Stud. Math. 174, No. 3, pp. 277 - 308, - 2006
• V. Knopova. " Continuity of certain pseudo-differential operators in the spaces of generalized smoothness. ". Ukr. Mat. Zh. 58 (5) , pp. 638 - 652, - 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. 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
• 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. "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. 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
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

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