Nikolay Kachanovsky

@imath.kiev.ua

Institute of Mathematics of NAS of Ukaine



                    

https://researchid.co/nkachano

RESEARCH, TEACHING, or OTHER INTERESTS

Mathematics, Analysis, Statistics and Probability

12

Scopus Publications

410

Scholar Citations

13

Scholar h-index

19

Scholar i10-index

Scopus Publications

  • Wick multiplication and its relationship with integration and stochastic differentiation on spaces of nonregular test functions in the Lévy white noise analysis
    N.A. Kachanovsky
    Vasyl Stefanyk Precarpathian National University
    We deal with spaces of nonregular test functions in the Lévy white noise analysis, which are constructed using Lytvynov's generalization of a chaotic representation property. Our goal is to study properties of a natural multiplication $-$ a Wick multiplication on these spaces, and to describe the relationship of this multiplication with integration and stochastic differentiation. More exactly, we establish that the Wick product of nonregular test functions is a nonregular test function; show that when employing the Wick multiplication, it is possible to take a time-independent multiplier out of the sign of a generalized stochastic integral; establish an analog of this result for a Pettis integral (a weak integral); obtain a representation of the generalized stochastic integral via formal Pettis integral from the Wick product of the original integrand by a Lévy white noise; and prove that the operator of stochastic differentiation of first order on the spaces of nonregular test functions satisfies the Leibnitz rule with respect to the Wick multiplication.

  • On Wick calculus and its relationship with stochastic integration on spaces of regular test functions in the Lévy white noise analysis
    N.A. Kachanovsky
    Vasyl Stefanyk Precarpathian National University
    We deal with spaces of regular test functions in the Lévy white noise analysis, which are constructed using Lytvynov's generalization of a chaotic representation property. Our aim is to study properties of Wick multiplication and of Wick versions of holomorphic functions, and to describe a relationship between Wick multiplication and integration, on these spaces. More exactly, we establish that a Wick product of regular test functions is a regular test function; under some conditions a Wick version of a holomorphic function with an argument from the space of regular test functions is a regular test function; show that when employing the Wick multiplication, it is possible to take a time-independent multiplier out of the sign of an extended stochastic integral with respect to a Lévy process; establish an analog of this result for a Pettis integral (a weak integral); obtain a representation of the extended stochastic integral via formal Pettis integral from the Wick product of the original integrand by a Lévy white noise. As an example of an application of our results, we consider an integral stochastic equation with Wick multiplication.

  • On the relationship between Wick calculus and stochastic integration in the Lévy white noise analysis
    Maria M. Frei and Nikolai A. Kachanovsky
    Springer Science and Business Media LLC

  • Interconnection between wick multiplication and integration on spaces of nonregular generalized functions in the lévy white noise analysis
    N.A. Kachanovsky and T.O. Kachanovska
    Vasyl Stefanyk Precarpathian National University
    We deal with spaces of nonregular generalized functions in the Lévy white noise analysis, which are constructed using Lytvynov's generalization of a chaotic representation property. Our aim is to describe a relationship between Wick multiplication and integration on these spaces. More exactly, we show that when employing the Wick multiplication, it is possible to take a time-independent multiplier out of the sign of an extended stochastic integral; establish an analog of this result for a Pettis integral (a weak integral); and prove a theorem about a representation of the extended stochastic integral via the Pettis integral from the Wick product of the original integrand by a Lévy white noise. As examples of an application of our results, we consider some stochastic equations with Wick type nonlinearities.

  • Some remarks on operators of stochastic differentiation in the Lévy white noise analysis



  • Stochastic integral of Hitsuda-Skorokhod type on the extended Fock space
    N. A. Kachanovsky and V. A. Tesko
    Springer Science and Business Media LLC

  • An extended stochastic integral and a wick calculus on parametrized Kondratiev-type spaces of meixner white noise
    N. A. KACHANOVSKY
    World Scientific Pub Co Pte Ltd
    Using a general approach that covers the cases of Gaussian, Poissonian, Gamma, Pascal and Meixner measures, we consider an extended stochastic integral and construct elements of a Wick calculus on parametrized Kondratiev-type spaces of generalized functions; consider the interconnection between the extended stochastic integration and the Wick calculus; and give an example of a stochastic equation with a Wick-type nonlinearity. The main results consist of studying the properties of the extended (Skorohod) stichastic integral subject to the particular spaces under consideration; and of studying the properties of a Wick product and Wick versions of holomorphic functions on the parametrized Kondratiev-type spaces. These results are necessary, in particular, in order to describe properties of solutions of normally ordered white noise equations in the "Meixner analysis".



  • On orthogonal appell-like polynomials in non-Gaussian analysis
    A. A. Kalyuzhnyi and N. A. Kachanovskii
    Springer Science and Business Media LLC

  • Biorthogonal appell systems in analysis on co-nuclear spaces
    N. A. Kachanovsky and G. F. Us
    Springer Science and Business Media LLC

RECENT SCHOLAR PUBLICATIONS

  • Елементи аналізу Леві на просторах нерегулярних основних та узагальнених функцій
    N Kachanovsky
    Ukrains’ kyi Matematychnyi Zhurnal 76 (12), 1752–1782-1752–1782 2024

  • Wick multiplication and its relationship with integration and stochastic differentiation on spaces of nonregular test functions in the Lvy white noise analysis
    NA Kachanovsky
    Carpathian Mathematical Publications 16 (1), 61-83 2024

  • On Wick calculus and its relationship with stochastic integration on spaces of regular test functions in the Lvy white noise analysis
    NA Kachanovsky
    Carpathian Mathematical Publications 14 (1), 194-212 2022

  • On the relationship between Wick calculus and stochastic integration in the Lvy white noise analysis
    MM Frei, NA Kachanovsky
    European Journal of Mathematics 6 (1), 179-196 2020

  • Interconnection between Wick multiplication and integration on spaces of nonregular generalized functions in the Lvy white noise analysis
    NA Kachanovsky, TO Kachanovska
    Carpathian Mathematical Publications 11 (1), 70-88 2019

  • On Wick calculus on spaces of nonregular generalized functions of Lvy white noise analysis
    NA Kachanovsky
    Карпатські математичні публікації, 114-132 2018

  • Some remarks on operators of stochastic differentiation in the Lvy white noise analysis
    MM Frei, NA Kachanovsky
    Methods of Functional Analysis and Topology 23 (04), 320-345 2017

  • Operators of stochastic differentiation on spaces of nonregular generalized functions of Lvy white noise analysis
    NA Kachanovsky
    Карпатські математичні публікації, 83-106 2016

  • Operators of stochastic differentiation on spaces of nonregular test functions of Lvy white noise analysis
    NA Kachanovsky
    Methods of Functional Analysis and Topology 21 (04), 336-360 2015

  • On operators of stochastic differentiation on spaces of regular test and generalized functions of Lvy white noise analysis
    MM Dyriv, NA Kachanovsky
    Carpathian Mathematical Publications 6 (2), 212-229 2014

  • On Kondratiev spaces of test functions in the non-Gaussian infinite-dimensional analysis
    NA Kachanovsky
    Methods of Functional Analysis and Topology 19 (04), 301-309 2013

  • On extended stochastic integrals with respect to Lvy processes
    NA Kachanovsky
    Carpathian Mathematical Publications 5 (2), 256-278 2013

  • Розширені стохастичні інтеграли за процесом Леві на просторах узагальнених функцій
    М Качановський
    Математичний вісник Наукового товариства ім. Шевченка 10 (1-2), 169-188 2013

  • Stochastic integrals with respect to a Levy process and stochastic derivatives on spaces of regular test and generalized functions
    MM Dyriv, NA Kachanovsky
    Наукові вісті Національного технічного університету України Київський 2013

  • Extended stochastic integrals with respect to a Lvy processes on spaces of generalized functions
    NA Kachanovsky
    Math. Bulletin of Taras Shevchenko Sci. Society, 169-188 2013

  • Стохастичні інтеграли по процесу Леві та стохастичні похідні на просторах регулярних основних і узагальнених функцій
    MM Dyriv, NA Kachanovsky
    Наукові вісті Національного технічного університету України" Київський 2013

  • Clark-Ocone type formulas on spaces of test and generalized functions of Meixner white noise analysis
    NA Kachanovsky
    Methods of Functional Analysis and Topology 18 (02), 160-175 2012

  • Stochastic Integral and Stochastic Derivative Connected with a Lvy Progress
    NO Kachanovsky
    НТУУ КПІ 2012

  • Notes on Wick calculus on parametrized test functions spaces of Meixner white noise
    NA Kachanovsky
    Methods of Functional Analysis and Topology 17 (02), 150-167 2011

  • Clark-Ocone type formulas in the Meixner white noise analysis
    NA Kachanovsky
    Carpathian Mathematical Publications 3 (1), 56–72-56–72 2011

MOST CITED SCHOLAR PUBLICATIONS

  • On an extended stochastic integral and the Wick calculus on the connected with the generalized Meixner measure Kondratiev-type spaces
    NA Kachanovsky
    Methods of Functional Analysis and Topology 13 (04), 338-379 2007
    Citations: 31

  • Minimality of Appell-like systems and embeddings of test function spaces in a generalization of white noise analysis
    NA Kachanovsky, SV Koshkin
    Methods of Functional Analysis and Topology 5 (03), 13-25 1999
    Citations: 24

  • On extended stochastic integrals with respect to Lvy processes
    NA Kachanovsky
    Carpathian Mathematical Publications 5 (2), 256-278 2013
    Citations: 23

  • Biorthogonal Appell-like systems in a Hilbert space
    NA Kachanovsky
    Methods of Functional Analysis and Topology 2 (03), 36-52 1996
    Citations: 23

  • Extended stochastic integrals with respect to a Lvy processes on spaces of generalized functions
    NA Kachanovsky
    Math. Bulletin of Taras Shevchenko Sci. Society, 169-188 2013
    Citations: 20

  • Stochastic integral of Hitsuda–Skorokhod type on the extended Fock space.
    N Kachanovsky, V Tesko
    Ukrainian Mathematical Journal 61 (6) 2009
    Citations: 20

  • An extended stochastic integral and a Wick calculus on parametrized Kondratiev-type spaces of Meixner white noise
    NA Kachanovsky
    Infinite Dimensional Analysis, Quantum Probability and Related Topics 11 (04 2008
    Citations: 17

  • On an extended Malliavin derivative connected with the Poisson-and Gamma-measures
    NA Kachanovsky
    Methods of Functional Analysis and Topology 9 (03), 213-240 2003
    Citations: 16

  • On the extended stochastic integral connected with the gamma-measure on an infinite-dimensional space
    NA Kachanovsky
    Methods of Functional Analysis and Topology 8 (02), 10-32 2002
    Citations: 16

  • Generalized stochastic derivatives on parametrized spaces of regular generalized functions of Meixner white noise
    NA Kachanovsky
    Methods of Functional Analysis and Topology 14 (04), 334-350 2008
    Citations: 15

  • Dual Appell-like systems and finite order spaces in non-Gaussian infinite dimensional analysis
    NA Kachanovsky
    Methods of Functional Analysis and Topology 4 (02), 41-52 1998
    Citations: 15

  • A generalized stochastic derivative on the Kondratiev-type space of regular generalized functions of Gamma white noise
    NA Kachanovsky
    Methods of Functional Analysis and Topology 12 (04), 363-383 2006
    Citations: 14

  • Generalized stochastic derivatives on a space of regular generalized functions of Meixner white noise
    NA Kachanovsky
    Methods of Functional Analysis and Topology 14 (01), 32-53 2008
    Citations: 13

  • Operators of stochastic differentiation on spaces of nonregular test functions of Lvy white noise analysis
    NA Kachanovsky
    Methods of Functional Analysis and Topology 21 (04), 336-360 2015
    Citations: 12

  • On operators of stochastic differentiation on spaces of regular test and generalized functions of Lvy white noise analysis
    MM Dyriv, NA Kachanovsky
    Carpathian Mathematical Publications 6 (2), 212-229 2014
    Citations: 12

  • Stochastic integrals with respect to a Levy process and stochastic derivatives on spaces of regular test and generalized functions
    MM Dyriv, NA Kachanovsky
    Наукові вісті Національного технічного університету України Київський 2013
    Citations: 12

  • On biorthogonal approach to construction of non-Gaussian analysis and application to Poisson analysis on configuration space
    NA Kachanovsky
    Methods of Functional Analysis and Topology 6 (02), 13-21 2000
    Citations: 11

  • On analog of stochastic integral and Wick calculus in non-Gaussian infinite dimensional analysis
    NA Kachanovsky
    Methods of Functional Analysis and Topology 3 (03), 1-12 1997
    Citations: 11

  • An extended stochastic integral and the Wick calculus on the connected with the Gammameasure spaces of regular generalized functions
    NA Kachanovsky
    Ukr. Math. J 57 (8), 1030-1057 2005
    Citations: 10

  • Stochastic Integral and Stochastic Derivative Connected with a Lvy Progress
    NO Kachanovsky
    НТУУ КПІ 2012
    Citations: 9