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Department of Probability Theory,
Statistics
and Actuarial Mathematics

Mechanics and Mathematics
faculty

prob.stat.act@gmail.com, probability@univ.kiev.ua
Tel/Fax: +38 (044) 259 03 92

   

Mykola Portenko


Education:
  • Doctor of Sciences in Mathematics (1978, Institute of Mathematics of Ukrainian National Academy of Sciences.) The title of dissertation: Generalized Diffusion Processes.
  • University degree: Diploma of Higher Education from Kyiv University, Ukraine, 1963.
  • Speciality: Mathematician. Specialist in Probability Theory and Mathematical Statistics.
Areas of research and interest:
  • Stochastic differential equations
  • Diffusion processes
  • Markov processes
  • Limit theorems for stochastic processes
  • Random walks
Professional Activities:
  • Editor of the Journal ďTheory of Stochastic ProcessesĒ
Societies:
  • Associate member of Ukrainian National Academy of Sciences
  • Member of Kyiv Mathematical Society

Conferences


    Publications

      • Textbooks and tutorials
        • Korolyuk, V. (ed.); Portenko, N. (ed.); Syta, H. (ed.) "Skorokhodís ideas in probability theory. ". Proceedings of the Institute of Mathematics of the National Academy of Sciences of Ukraine. Mathematics and its Applications. 32. Kyïv: Institute of Mathematics of NAS of Ukraine., 336 p. - 2000
        • Portenko, M.I. "Diffusion processes in media with membranes. (Protsesi difuzīï v seredovishchakh z membranami.) ". Trudi Institutu Matematiki Natsīonalínoï Akademīï Nauk Ukraïni. 10. Kiev: Īnstitut Matematiki NAN Ukraïni., 200 p. - 1995
        • Portenko, N.I. "Diffusion in media with semi-transparent membranes. (Difuzīya v seredovishchakh z napīvprozorimi membranami.)". Trudi Institutu Matematiki Natsīonalínoï Akademīï Nauk Ukraïni. 8. Kiïv: Institut Matematiki NAN Ukraïni., 136 p. - 1994
        • Portenko, N.I. "Generalized diffusion processes. Transl. from the Russian by H. H. McFaden.". Translations of Mathematical Monographs, 83. Providence, RI: American Mathematical Society (AMS)., 180 p. - 1990
        • Portenko, N.I.; Skorokhod, A.V.; Shurenkov, V.M. "Markov processes.". Itogi Nauki Tekh., Ser. Sovrem. Probl. Mat., Fundam. Napravleniya 46, 248 p. - 1989
        • Korolyuk, V.S.; Portenko, N.I.; Skorokhod, A.V.; Turbin, A.F. "A manual on probability theory and mathematical statistics. (Spravochnik po teorii veroyatnostej i matematicheskoj statistike). 2nd ed., rev. and compl.". Moskva: "Nauka". Glavnaya Redaktsiya Fiziko-Matematicheskoj Literatury., 640 p. - 1985
        • Korolyuk, V.S.; Portenko, N.I.; Skorokhod, A.V.; Turbin, A.F. "Aide-mémoire de théorie des probabilités et de statistique mathématique. Traduit du russe par Djilali Embarek.". Moscou: Editions Mir., 581 p. - 1983
        • Portenko, N.I. "Generalized diffusion processes. (Obobshchennye diffuzionnye protsessy.)". Kiev: Naukova Dumka., 208 p. - 1982
        • Gikhman, I.I. (ed.); Liníkov, Yu.N. (ed.); Danilyuk, I.I. (ed.); Portenko, N.I. (ed.); Skorokhod, A.V. (ed.) "Theory of stochastic processes. 3. (Teoriya sluchajnykh protsessov. Vypusk 3).". Respublikanskii mezhvedomstvennyi sbornik. Kiev: "Naukova Dumka"., 160 p. - 1975
        • Gikhman, I.I. (ed.); Liníkov, Ju.N. (ed.); Danilyuk, I.I. (ed.); Portenko, N.I. (ed.); Skorokhod, A.V. (ed.) "Theory of random processes. 2. (Teoriya sluchajnykh protsessov. Vypusk 2).". Respublikanskii mezhvedomstvennyi sbornik. Kiev: "Naukova Dumka". , 140 p. - 1974

      • Articles
        • 2007
          • Aryasova, Olga V.; Portenko, Mykola I. "One example of a random change of time that transforms a generalized diffusion process into an ordinary one.". Theory Stoch. Process. 13(29), No. 3, pp. 12 - 21, - 2007
          2006
          • Kopytko, Bogdan I.; Portenko, Mykola I. "An example of a stochastic differential equation with the property of weak non-uniqueness of a solution.". Theory Stoch. Process. 12, No. 28, Part 1-2, pp. 68 - 76, - 2006
          2005
          • Aryasova, Olga V.; Portenko, Mykola I. "One class of multidimensional stochastic differential equations not having the property of weak uniqueness of a solution.". Theory Stoch. Process. 11, No. 27, Part 3-4, pp. 14 - 28, - 2005
          • Kopytko, Bogdan I.; Portenko, Mykola I. "One more example of a diffusion process whose local characteristics do not determine uniquely its transition probability.". Theory Stoch. Process. 11, No. 27, Part 1-2, pp. 74 - 80, - 2005
          • Portenko, M.I. "On renewal equations appearing in some problems in the theory of generalized diffusion processes. ". Ukr. Mat. Zh. 57, No. 9, pp. 1302 - 1312, - 2005
          • Portenko, M.I.; Kopytko, B.I. "The example of a diffusion process, whose Kolmogorov local characteristics do not determine uniquely its transition probabilities.". Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 2005, No. 5, pp. 25 - 32, - 2005
          2003
          • Aryasova, Olga V.; Portenko, Mykola I. "Two-dimensional Brownian motion with membranes situated on the sides of an angle.". Theory Stoch. Process. 9(25), No. 1-2, pp. 18 - 29, - 2003
          2000
          • Arjasova, O.V.; Portenko, M.I. "The Wiener process on the plane with membranes located on two straight lines as an oblique product of two random processes of a module and a phase.". Nelinijni Kolyvannya 3, No.1, pp. 7 - 12, - 2000
          • Portenko, Mykola I.; Salehi, Habib; Skorokhod, Anatolii V. "On large deviations for dynamical systems randomly perturbed by a fast Markov process.". Theory Stoch. Process. 6(22), No.1-2, pp. 125 - 135, - 2000
          • Portenko, N.I. "A probabilistic representation for the solution of a problem of mathematical physics.". Ukr. Math. J. 52, No.9, pp. 1457 - 1469, - 2000
          • Kovalenko, I.M.; Korolyuk, V.S.; Portenko, M.I.; Samojlenko, A.M.; Syta, G.M.; Yadrenko, M.I. "Anatolij Vladimirovich Skorokhod (on his 70th birthday).". Ukr. Math. J. 52, No.9, pp. 1321 - 1323, - 2000
          1999
          • Portenko, N.; Salehi, H.; Skorokhod, A. "Filtering in multitarget systems with discrete time observations.". Random Operators \& Stoch. Equat. 7, pp. 207 - 214, - 1999
          1998
          • Portenko, N.; Salehi, A.; Skorokhod, A. "Optimal filtering in target tracking in presence of uniformly distributed errors and false targets. ". Random Operators \& Stoch. Equat. 6, pp. 213 - 240, - 1998
          • Portenko, Nikolaj I. "On multidimensional skew Brownian motion and the Feynman-Kac formula.". Theory Stoch. Process. 4(20), No.1-2, pp. 60 - 70, - 1998
          • Durdyev, A.K.; Portenko, M.I. "On the number of crossings of an elastic absorbing membrane on a hyperplane by a Brownian motion. ". Theory Probab. Math. Stat. 56, pp. 67 - 80, - 1998
          1997
          • Portenko, N.; Salehi, H.; Skorokhod, A. "On optimal filtering of multitarget tracking systems based on point processes observations. ". Random Operators \& Stoch. Equat. 5, pp. 1 - 34, - 1997
          • Portenko, Nikolai I. "One class of transformations of a symmetric stable process.". Theory Stoch. Process. 3(19), No.3-4, pp. 373 - 387, - 1997
          1996
          • Portenko, N.I. "On some perturbations of symmetric stable processes.". Watanabe, S. (ed.) et al., Probability theory and mathematical statistics. Proceedings of the seventh Japan-Russia symposium, Tokyo, Japan, July 26-30, 1995. Singapore: World Scientific., pp. 414 - 422, - 1996
          • Portenko, Nikolai I. "On some transformations of the transition probability density of a symmetric stable process.". Theory Stoch. Process. 2(18), No.1-2, pp. 74 - 80, - 1996
          • Portenko, Nikolai "Diffusion in a medium with semi-transparent diaphragms.". Engelbert, Hans-Jürgen (ed.) et al., Stochastic processes and related topics. Proceedings of the 10th winter school, Siegmundsberg, Germany, March 13‒19, 1994. Amsterdam: Gordon and Breach Publishers. Stochastics Monogr. 10, pp. 117 - 128, - 1996
          • Löbus, J.-U.; Portenko, M.I. "On a class of perturbed generators of stable processes.". Theory Probab. Math. Stat. 52, pp. 109 - 119, - 1996
          • Löbus, J.-U.; Portenko, M.I. "On a class of perturbed generators of stable processes.". Theory Probab. Math. Stat. 52, pp. 109 - 119, - 1996
          1995
          • Durdiyev, A.K.; Portenko, N.I. "The number of crossings through a hyperplane by some generalized diffusion process.". Exploring Stochastic Laws, pp. 121 - 128, - 1995
          • Portenko, N.I.; Spivak, G.L. "Hilbert space valued Brownian motion with partial reflection on a hyperplane.". Àrato, M. (ed.) et al., New trends in probability and mathematical statistics. Proceedings of the second Ukrainian-Hungarian conference, Mukachevo, Ukraine, September 25-October 1, 1992. Kiev: TViMS. Teor. Veroyatn. Mat. Stat./Probab. Theory Math. Stat. 2, pp. 410 - 416, - 1995
          • Portenko, N.I. "The development of I. I. Gikhamís idea concerning the methods for investigating local behavior of diffusion processes and their weakly convergent sequences.". Theory Probab. Math. Stat. 50, pp. 7 - 22, - 1995
          • Podolynny, S.I.; Portenko, N.I. "On multidimensional stable processes with locally unbounded drift.". Random Oper. Stoch. Equ. 3, No.2, pp. 113 - 124, - 1995
          1994
          • Portenko, N.I. "Some perturbations of drift-type for symmetric stable processes.". Random Oper. Stoch. Equ. 2, No.3, pp. 211 - 224, - 1994
          • Goshko, L.V.; Portenko, N.I. "Limit theorems for the number of crossings of a fixed plane by certain sequences of generalized diffusion processes.". Ukr. Math. J. 46, No.4, pp. 373 - 388, - 1994
          • Portenko, Nikolai "Diffusion processes in a medium with semi-transparent diaphragms.". Portenko, M. I. (ed.) et al., Some problems of the modern theory of differential equations. Kiev: Ukrainian National Academy of Sciences. Institute of Mathematics, Natl. Acad. Sci. Ukr., Kiev (UA). Inst. Math. Prepr. 94.29, pp. 3 - 13, - 1994
          1993
          • Goshko, L.V.; Portenko, M.I. "Limit theorems for a number of intersections of some surface by a sequence of diffusion processes. ". Dopov. Akad. Nauk Ukr. 1993, No.6, pp. 29 - 34, - 1993
          1992
          • Portenko, N.I. "On the theory of diffusion processes.". Shiryaev, A. N. (ed.) et al., Probability theory and mathematical statistics. Proceedings of the 6th USSR-Japan symposium, Kiev, USSR, 5-10 August, 1991. Singapore: World Scientific., pp. 259 - 267, - 1992
          1990
          • Korolyuk, V.S.; Portenko, N.I. "A. V. Skorokhodís investigations in the area of limit theorems for random processes and the theory of stochastic differential equations.". Ukr. Math. J. 42, No.9, pp. 1029 - 1040, - 1990
          1989
          • Efimenko, S.V.; Portenko, N.I. "On the distribution of the number of intersections of a delay screen by a process sewn of two processes of Brownian motion.". Stochastic analysis and its application, Collect. Sci. Works, Kiev, pp. 55 - 63, - 1989
          • Efimenko, S.V.; Portenko, N.I. "On the number of intersections of a fixed level by a stochastic process. ". Statistics and control of stochastic processes, Collect. Artic., Moskva, pp. 70 - 75, - 1989
          • Efimenko, S.V.; Portenko, N.I. "Sojourn time type functionals of a process obtained by pasting together two Brownian motion processes.". Ukr. Math. J. 41, No.1, pp. 25 - 29, - 1989
          1988
          • AlíFarahk, Kh.; Portenko, N.I. "On the number of crossings of a fixed level by a transient diffusion process.". Selected problems of the modern theory of stochastic processes, Collect. Sci. Works, pp. 4 - 12, - 1988
          1987
          • Portenko, N.; Yefimenko, S. "On the number of crossings of a partly reflecting hyperplane by a multidimensional Wiener process. ". Stochastic differential systems, Proc. IFIP-WG 7/1 Work. Conf., Eisenach/GDR 1986, Lect. Notes Control Inf. Sci. 96, pp. 194 - 203, - 1987
          1986
          • Efimenko, S.V.; Portenko, N.I. "On the number of intersections of a partially reflecting screen by a Wiener process.". Probabilistic methods for the investigation of systems with an infinite number of degrees of freedom, Collect. sci. Works, pp. 57 - 64, - 1986
          • Portenko, N.I. "On the theory of the generalized diffusion.". Stochastic differential systems, Proc. 3rd Bad Honnef Conf. 1985, Lect. Notes Control Inf. Sci. 78, pp. 330 - 341, - 1986
          1985
          • Mirzoeva, T.M.; Portenko, N.I. "Limit theorems for functionals of irreversible random walks.". Ukr. Math. J. 37, pp. 55 - 63, - 1985
          • Mirzoeva, T.M.; Portenko, N.I. "Limit theorems for functionals of transient random walks.". Ukr. Mat. Zh. 37, No.1, pp. 64 - 74, - 1985
          • Lobanov, K.A.; Portenko, N.I. "Limit theorem for random walks with reflection.". Stochastic processes. Theory and practice, Collect. sci. Works, pp. 72 - 82, - 1985
          1984
          • Mirzoeva, T.M.; Portenko, N.I. "Limit distribution of functionals of non-recurrent random walks turning into the recurrent ones at the limit. ". Some questions of the theory of stochastic processes, Collect. sci. Works, pp. 79 - 96, - 1984
          1983
          • Mirzoeva, T.M.; Portenko, N.I. "Asymptotic expansion of the potential kernel for a class of transient random walks.". Problems of the theory of probability distributions, Collect. sci. Works, pp. 78 - 92, - 1983
          • Kopytko, B.I.; Portenko, N.I. "Analytical methods of pasting together of diffusion processes.". Probability theory and mathematical statistics, Proc. 4th USSR-Jap. Symp., Tbilisi/USSR 1982, Lect. Notes Math. 1021, pp. 318 - 326, - 1983
          1982
          • Kopytko, B.I.; Portenko, N.I. "A remark concerning the processes sewn of two processes of Brownian motion.". Some questions of the theory of stochastic processes, Collect. sci. Work Kiev, pp. 67 - 79, - 1982
          1981
          • Mirzoeva, T.M.; Portenko, N.I. "On the kernel of the potential of an irreversible random walk.". Probabilistic infinite dimensional analysis, Collect. sci. Works, pp. 74 - 83, - 1981
          1980
          • Portenko, N.I. "Stochastic differential equations with generalized drift vector.". Theory Probab. Appl. 24, pp. 338 - 353, - 1980
          1979
          • Portenko, N.I. "Diffusion processes with generalized drift coefficients. ". Theory Probab. Appl. 24, pp. 62 - 78, - 1979
          • Portenko, N.I. "Stochastic differential equations with generalized drift vector.". Teor. Veroyatn. Primen. 24, pp. 332 - 347, - 1979
          • Portenko, N.I. "Diffusion processes with generalized drift coefficient.". Teor. Veroyatn. Primen. 24, pp. 62 - 77, - 1979
          1976
          • Portenko, N.I. "Generalized diffusion processes.". Proc. 3rd Japan-USSR Symp. Probab. Theory, Taschkent 1975, Lect. Notes Math. 550, pp. 500 - 523, - 1976
          • Portenko, N.I. "Zur Theorie der stochastischen Differentialgleichungen.". Theory of Random Proc., Vol. 4, pp. 72 - 80, - 1976
          • Portenko, N.I. "Some limit theorems for additive functionals of processes with independent increments.". Theor. Probab. math. Statist. 4 , pp. 121 - 126, - 1976
          1975
          • Portenko, N.I. "Diffusion processes with unbounded drift coefficient. ". Theory Probab. Appl. 20, pp. 27 - 37, - 1975
          • Portenko, N.I. "On the existence of solutions of stochastic differential equations with integrable drift coefficient. ". Theory Probab. Appl. 19, pp. 552 - 557, - 1975
          1974
          • Portenko, N.I. "Asymptotic behavior of the kernel of the potential of a one-dimensional irreversible random walk. ". Ukr. Math. J. 26, pp. 18 - 26, - 1974
          • Portenko, N.I. "Über Grenzwertsätze für Funktionale von Markovschen Ketten ohne Rückkehr.". Teor. slucain. Process., respubl. mezvedomst. Sbornik 2, pp. 73 - 80, - 1974
          • Portenko, N.I.; Prokopenko, L.N. "A method of proving limit theorems for functionals of random walks.". Theor. stoch. Processes, No.1, pp. 122 - 135, - 1974
          1973
          • Portenko, N.I. "Nichtnegative adaptive Funktionale Markovscher Prozesse und einige Grenzwertsaetze.". Teor. slucain. Process. 1, pp. 86 - 107, - 1973
          • Portenko, N.I.; Prokopenko, L.N. "Über eine Methode zum Beweis von Grenzwertsätzen für Funktionale von Irrfahrten.". Teor. slucain. Process. 1, pp. 107 - 119, - 1973
          1971
          • Portenko, N.I. "Integro-differential equations for probability distributions of additive functionals of diffusion processes. ". Select. Translat. Math. Statist. Probab. 9, pp. 299 - 310, - 1971
          • Portenko, N.I. "Some limit theorems for additive functionals of processes with independent increments.". Teor. Veroyatn. Mat. Stat. 4, pp. 130 - 136, - 1971
          1970
          • Portenko, N.I. "Additive functionals of Markow processes and potentials.". Mat. Fiz., Respubl. Mezhvedomstv. Sb. 7, pp. 147 - 152, - 1970
          1968
          • Portenko, N.I. "On the existence of one class of additive functionals of diffusion processes.". Ukr. Math. J. 20, pp. 583 - 589, - 1968
          1967
          • Portenko, N.I. "Integral equations and limit theorems for additive functionals of a Markov process.". Theor. Probab. Appl. 12, pp. 500 - 505, - 1967
          1966
          • Portenko, N.I. "Über Integrodifferentialgleichungen für Wahrscheinlichkeitsverteilungen additiver Funktionale von Diffusionsprozessen.". Ukr. Mat. Zh. 18, No.5, pp. 60 - 68, - 1966

        First name: Mykola
        Surname: Portenko
        Date of birth: 23 February 1942
        Place of birth: Kalynivka, Cherkassky region, Ukraine
        Citizenship: Ukraine
        Address:
        Institute of Mathematics of Ukrainian National Academy of Sciences
        3, Tereshchenkivska St., 01601 Kyiv, Ukraine
        E-mail: portenko@imath.kiev.ua
        Tel: +380 44 224-53-72
        Fax: +380 44 224-53-72
        Languages: Ukrainian, Russian and English
        Current position:
        Chairman of the Department of the theory of stochastic processes, Institute of Mathematics of Ukrainian National Academy of Sciences
        Chairman of the Department of the theory of stochastic processes, Institute of Mathematics of Ukrainian National Academy of Sciences
        Professor of the Department of Probability Theory, Statistics ans Actuarial Mathematics at Kyiv University