Mykola Portenko

List of publications of a journal type

1. On integro-differential equations for the distribution of an additive functional of a diffusion process (in Russian). Ukrainian mathem.journ., vol.19, No.5, 1966.
2. Integral equations and some limit theorems for additive functionals of a Markov process (in Russian). Theor.Probab.and Appl., vol.12, No.3, 1967.
3. On the existence of a class of additive functionals of a diffusion process (in Russian). Ukrainian mathem.journ., vol.20, No.5, 1968.
4. Some limit theorems for additive functionals of a process with independent incre-ments (in Russian). Theor.Probab. and Mathem.Stat., No.4, 1971.
5. Non-negative additive functionals of a Markov process and some limit theorems (in Russian). Teor.Sluchainych Protsessov, vyp.l, Naukova dumka, Kyiv, 1973.
6. On a method for proving limit theorems for functionals of a random walk (in Rus-sian). Teor.Sluchainych Protsessov, vyp.l, Naukova dumka, Kyiv, 1973. (Co-author: L.N.Prokopenko).
7. On limit theorems for functionals of a transient Markov chain (in Russian). Teor.Sluchainych Protsessov, vyp.2, Naukova dumka, Kyiv, 1974.
8. On asymptotic behaviour of a potential kernel of one-dimensional random walk (in Russian). Ukrainian mathem.journ., vol.26, No.l, 1974.
9. On the existence of a solution to a stochastic differential equation with an integrable drift coefficient (in Russian). Theor.Probab.and Appl., vol.19, No.3, 1974.
10. On the Cauchy problem for second-order parabolic equations (in Russian). Teor.Sluchainych Protsessov, vyp.3, Naukova dumka, Kyiv, 1975.
11. On the theory of stochastic differential equations (in Russian). Teor. Sluchainych Protsessov, vyp.4, Naukova dumka, Kyiv, 1976.
12. Diffusion processes with an unbounded drift coefficient (in Russian). Theor.Probab.and Appl., vol.20, No.l, 1975.
13. Diffusion processes with irregular drift (in Russian). Proc.School and Sem.Theory of Random Processes (Druskininkai, 1974), Part II, Inst.Fiz.i Mat.Akad.Nauk Litovsk. SSR, Vilnius, 1975.
14. On the existence of e-optimal Markovian strategies for a controlled diffusion process (in Russian). Institute of Mathematics of Ukrainian Acad.of Sci., 1973. (Co-author: A.V.Skorokhod).
15. Generalized diffusion processes. Lecture Notes in Mathematics, Vol.550, Springer Verlag, Berlin-Heidelberg-New York, 1976.
16. Diffusion processes with generalized drift coefficient (in Russian). Theor.Probab.and Appl., vol.24, No.l, 1979.
17. Stochastic differential equation with a generalized drift vector (in Russian). Theor. Probab. and Appl., vol.24, No.2, 1979.
18. Analytic methods of pasting together diffusion processes. Lecture Notes in Math-ematics, vol.1021, Springer Verlag, Berlin-Heidelberg-New York, 1983. (Co-author: B.I.Kopytko).
19. Limit theorems for functionals of a transient random walk (in Russian). Ukrainian mathem.journ., vol.37, No.l, 1985. (Co-autor: T.M.Myrsoeva).
20. To the theory of generalized diffusion. Lecture Notes in Control and Information Sciences, 78, Springer Verlag, Berlin-Heidelberg-New York, 1986.
21. On the number of crossings of a partly reflecting hyperplane by a multidimensional Wiener process. Lecture Notes in Control and Information Sciences, vol.96, Springer Verlag, Berlin-Heidelberg-New York, 1987. (Co-author: S.V.Yephimenko).
22. On a class of functionals of a process that is a result of pasting together two Brownian motions (in Russian). Ukrainian mathem.journ., vol.41, No.l, 1989. (Co-author: S.V.Yephimenko).
23. On Skorokhod's investigations in limit theorems for stochastic processes and the theory of stochastic differential equations (in Russian). Ukrainian mathem.journ., vol.42, No.9, 1990. (Co-author: V.S.Korolyuk).
24. Anatolii Vladimirovich Skorokhod (to his 60th birthday) (in Russian). Uspekhi matem.nauk, vol.46, vyp.4, 1991. (Co-authors: V.S.Korolyuk, H.N. Sytaya).
25. On the theory of diffusion processes. Probability Theory and Mathematical Statis-tics, Proceedings of the Sixth USSR-Japan Symposium, Kiev, August 5-10, 1991. World Scientific, Singapore.
26. Hilbert space valued Brownian motion with partial reflection on a hyperplane. Pro-ceeding of II Ukr.-Hung.Conf., New Trends in Probability, Theory and Mathematical Statistics, VSP /TBiMC, Utrecht/ Kyiv, 1995.
27. Limit theorems for the number of crossings of a fixed hyperplane by some sequences of generalized diffusion processes (in Ukrainian). Ukrainian mathem.journ., vol.46, No.4, 1994. (Co-author: Goshko L.V.)
28. The development of Gikhman's idea to investigate the local behaviour of a diffusion process or a sequence of diffusion processes that is weakly converged (in Ukrainian). Theor.Probab.and Mathem.Stat., No.50, 1994.
29. Some perturbations of a drift type for symmetric stable processes. Random Opera-tors and Stochastic Equations, vol.2, No.3, 1994.
30. On multidimensional stable processes with locally unbounded drift. Random Oper-ators and Stochastic Equations, vol.3, No.2, 1995. (Co-author: S.I.Podolynny).
31. On a class of perturbations of the generator of a stable process (in Ukrainian). Theor.Probab.and Mathem.Stat., No.52, 1995. (Co-author: J.-U.Loebus).
32. Diffusion in a medium with semi-transparent diaphragms. Stochastic Processes and Related Topics. Edited by Hans J.Engelbert, Hans Folmer and Jerzy Zabchyk. Stochastic Monographs, vol.10, Gordon and Breach Publishers, 1996.

33. On some perturbations of symmetric stable processes. Probability Theory and Math-ematical Statistics. Proceedings of the Seventh Japan-Russia Symposium. World Scientific, Singapore, 1996.
34. On some transformations of the transition probability density of a symmenric stable process. Theory of Stochastic Processes, vol.2(18), No.1-2, 1996.
35. On optimal filtering of multitarget tracking systems based on point processes obser-vations. Random Operators and Stochastic Equations, vol.5, No.l, 1997. (Co-authors: H.Salehi, A.V.Skorokhod).
36. Optimal filtering in target tracking in presence of uniformly distributed errors and false targets. Random Operators and Stochastic Equations, vol.6, No.3, 1998. (Co-authors: H.Salehi, A.V.Skorokhod).
37. On the number of crossings of an elastic membrane situated on a hyperplane by a multidimensional Brownian motion (in Ukrainian). Theor.Probab. and Mathem.Stat., No.56, 1997. (Co-author: A.K.Durdyev).
38. On multidimensional skew Brownian motion and the Feynman-Kac formula. Theory of Stochastic Processes, vol.4(20), No.1-2, 1998.
39. One class of transformations of a symmetric stable process. Theory of Stochastic Processes, vol.3(19), 1997.
40. Filtering in multitarget systems with discrete time observations. Random Operators and Stochastic Equations, vol.7, No.3, 1999. (Co-authors: H.Salehi, A.V.Skorokhod).
41. A Wiener process on a plane with membranes on two intersecting straight lines as a skew product of two random processes: modulus and phase (in Ukrainian). Non-Linear Oscillations, vol.3. No. l. 2000 (Co-author: O V Aryasova).
42. A probabilistic representation of the solution to one problem of mathematical physics. Ukrainian mathem. Journal, vol. 52, №   9, 2000.
43. On large deviations for dynamical systems randomly perturbed by a fast Markov process, vol. 6 (22), no. 1-2, 2000.
44. On a multidimensional Brownian motion with a membrane located on a hyperplane and acting in an oblique direction. Ukrainian mathematical congress – 2001. Proceedings, Section 9 (co-author B.I.Kopytko).
45. Two-dimensional Brownian motion with membranes situated on the sides of an angle. Theory of stochastic Processes, vol. 9 (25), no. 1-2, 2003 (co-author O. Aryasova).
46. One more example of a diffusion process whose local characteristics do not determine uniquely its transition probability. Theory of Stochastic Processes, vol. 11 (27), no. 1-2, 2005  (co-author B.I.Kopytko).
47. On the renewal equations that arise in the theory of generalized diffusion processes. Ukrainian mathem. Journal, vol. 57, no. 9, 2005 (in Ukrainian).
48. One class of multidimensional stochastic differential equations having no property of weak uniqueness of a solution. Theory of Stochastic Processes, vol. 11 (27), no. 3-4, 2005  (co-author O. Aryasova).
49. An example of a stochastic differential equation with the property of weak non-uniqueness of a  solution. Theory of Stochastic Processes, vol. 12 (28), no. 1-2, 2006  (co-author B.I.Kopytko).
50. One example of a random change of time that transforms a generalized diffusion process into an ordinary one. Theory of Stochastic Processes, vol.13(29), no.3, 2007 (co-author: O. Aryasova).
51. A uniqueness theorem for the martingale problem describing a diffusion in media with membranes, Theory of Stochastic processes, vol.14(30), no.2, 2008, pp.1-9 (co-author O.V.Aryasova).
52.
One formula for the resolvent of a one-dimensional diffusion process and its application to limit theorems. Mathematics Today'08. Kyiv, 2008. (in Ukrainian).
53.
The problem of pasting together two diffusion processes and classical potentials. Theory of Stochastic Processes, vol.15(31), no.2, 2009 (co-author: B. Kopytko).
54. On convergence of the resolvents of certain sequence of diffusion processes. Mathematics Today'09. Kyiv, 2009. (in Ukrainian, co-author: M. Sergiyenko).
55. On the number of crossings of an arbitrary level by certain sequence of diffusion processes with periodic coefficients, Mathematical Studies, vol.33, no2, 2010, pp. 199-211 (co-author M.M. Osypchuk) (in Ukrainian)
56. The limit distribution of the local times at zero of some sequence of diffusion processes, Matematychnyi visnyk NTSh, vol. 8, 2011, pp. 167-183 (co-author M.M. Osypchuk) (in Ukrainian)
57. An extremum problem for some class of Brownian motions with drifts, Problemy Matematicheskogo Analiza (Problems in Mathematical Analysis), no. 61, October 2011, pp. 139-146. English translation in "Journal of Mathematical Sciences", vol. 179, no. 1, November 21, 2011, pp. 164-173 (co-author M.M. Osypchuk)
58. On Ornshtein-Uhlenbeck's measure of a Hilbert ball in the space of continuous functions, Theory of Stochastic Processes, vol.19(35), no.1, 2014, pp. 46-51 (co-author: M.M. Osypchuk).
59. One type of singular perturbations of a multidimensional stable process, Theory of Stochastic Processes, vol.19(35), no.2, 2014, pp. 42-51 (co-author: M.M. Osypchuk).
60. On single-layer potentials for one class of pseudo-differential equations, Ukra´n. Mat. Zh., vol.67, no.11, 2015, pp. 1512-1524 (co-author: M.M. Osypchuk). (in Ukrainian)