prof. dr hab. Bohdan Kopyko 19.07.2019 -
Imię: prof. dr hab. Bohdan Kopyko
Status: Użytkownik
Ostatnia aktualizacja: 05-10-2018 18:10:36
prof. dr hab.Bohdan Kopytko


pokój: 304, al. Armii Krajowej 21
tel.: (0-34) 3250-324
email:
Publikacje:

Publikacje za okres 2011 - 2018: artykuły naukowe
1. Bohdan Kopytko, Recurrence relations for two-channel queueing systems with Erlangian service times and hysteretic strategy of random dropping of customers /Yuriy Zhernovyi, Bohdan Kopytko // JAMCM 2018, 17(2), 93-103.

2. Bohdan Kopytko, Recurrence relations for two-channel clozed queueing systems with Erlangian service times / Bohdan Kopytko, Kostyantyn Zhernovyi // JAMCM 2018, 17(1), 37-48.


3. Bohdan Kopytko, Solution of one initial – boundary Wentzel problem for a parabolic equation with discontinuous coefficients by the boundary integral equation method /Bohdan Kopytko, Zhanneta Tsapovska // JAMCM 2017, 16(1), 51-62.

4. Bohdan Kopytko, Recurence relations for a multi cha)/ nnel closed queueing system with erlangian service times of second order / Yuriy Zhernovyi, Bohdan Kopytko // JAMCM 2017, 16(3), 123-128.

5. Bohdan Kopytko, Modeling of the diffusion phenomenon in media with membranes by generalized diffusion processes (Rozdział monografii) / Bohdan Kopytko, Roman Shevchuk // Selected Topics in Contemporary Mathematical Modeling 2017, 87-108 (Ed. A. Z. Grzybowski) The Publishing Offise of Czestochowa University of Technology

6. Bohdan Kopytko, Roman Shevchuk, One-dimensional diffusion processes in half-bounded domains with reflection and possible jump-like exit from a moving boundary, Journal of Applied Mathematics and Computational Mechanics 2016, 15(4), 71-82.

7. B. I. Kopytko. On Feller semigroups associated with one-dimensional diffusion processes with membranes / B. I. Kopytko and R. V. Shevchuk // Theory of Stochastic Processes, vol.21 (37), no.1, 2016, pp.31-44.

8. Kopytko Bohdan. Steady - state characteristics of three - channel queueing systems with Erlangian service times / Bohdan. Kopytko, Kostyantyn Zhernovyi // Journal of Applied Mathematics and Computational Mechanics. 2016. no. 15(3). 75 - 87.

9. B. Kopytko. Time - dependent shock acceleration of particles. Effect of the time - dependent injection, with application to supernova remnants / O. Petruk and B. Kopytko // MNRAS (2016), v. 462, p. 3104 - 3114.

10. Kopytko Bohdan. The potentials method for the M/G/1/m queue with customer dropping and hysteretic strategy of the service time change / Yuriy Zhernovyi, Bohdan. Kopytko, // Journal of Applied Mathematics and Computational Mechanics. 2016. no. 15(1), 197 - 210.

11. Yuriy Zhernovyi, Bohdan Kopytko, The potentials method for a closed queueing system with hysteretic strategy of the service time change , Journal of Applied Mathematics and Computational Mechanics, 2015, no. 14(2), 131-143.

12. Yuriy Zhernovyi, Bohdan Kopytko, Kostyantyn Zhernovyi, On characteristics of the Mθ/G/1/m and Mθ/G/1 queues with queue-size based packet dropping, Journal of Applied Mathematics and Computational Mechanics, 2014, 13(4), 163-175.

13. Bohdan Kopytko, Roman Shevchuk, One-dimensional diffusions in bounded domains with a possible jump-like exit from a sticky boundary, Journal of Applied Mathematics and Computational Mechanics 2014, 13(3), 101-114.

14. Yuriy Zhernovyi, Bohdan Kopytko, The system M2θ/G/1/m with threshold control of the arrival rate and service time, Journal of Applied Mathematics and Computational Mechanics 2014, 13(2), 149-163.

15. Yuriy Zhernovyi, Bohdan Kopytko, The queuing system M2X/M/n with hysteretic control of the input flow intensity, Journal of Applied Mathematics and Computational Mechanics 2014, 13(1), 149-161.

16. Yuriy Zhernovyi, Bohdan Kopytko, Kostyantyn Zhernovyi, The busy period for the Mθ/G/1/m system with service time dependent of the queue length, Journal of Applied Mathematics and Computational Mechanics 2013, 12(4), 127-133.

17. B.I. Kopytko, R.V. Shevchuk, One-dimensional diffusion processes in bounded domains with boundary conditions and conjugation condition of Feller-Wentzell, Bukovinian mathematical journal. 2013. - v.1, no.1-2. - p. 77-85.

18. Bohdan Kopytko, Roman Shevchuk, Diffusion in one-dimensional bounded domains with reflection, absorption and jumps at the boundary and at some interior point, Journal of Applied Mathematics and Computational Mechanics 2013, 12(1), 55-68.

19. P.P. Kononchuk and B.I. Kopytko, Semigroups of operators that describe a Feller processont the line, which is the result of pasting together two diffusion processes, Theor.Probability and Math. Statist. no.84, 2012, Pages 87-97. S 0094-9000 (2012) 00868-5. Article electronically published on july 31, 2012.

20. Bohdan Kopytko, Andriy Novosyadlo, Feller semigroup for diffusion processpiesewise - constant generalized diffusion matrix and generalized drift vector, Scientific Researcz of the Institute of Mathematics and Computer Science 2012, 4 (11), 75 - 84.
21. Mykola Portenko, Bohdan Kopytko, On constructing a multidimensional diffusion processwith a membrane located on a given hyperplane and acting in an oblique direction, Scientific Researcz of the Institute of Mathematics and Computer Science 2012, 3 (11), 137 - 147.

22. B. I. Kopytko, R. V. Shevchuk. On pasting together two inhomogeneous diffusion processes on a line with the general Feller-Wentzell conjugation condition // Theory of Stochastic Processes, V. 17 (33), 2011, no. 2, pp. 55-70.

23. Bohdan Kopytko, Kostyantyn Zhernovyi, Stationary characteristics of gueue with switching of service modes .// Scientific Research of the Institute of Mathematics and Computer Science 2011, 2(10), 117-129.

24. K. Zhernovyi, B. Kopytko, Stationary characteristics and queueing systems with dual-speed service // Visnyk Chernivtsi Univ. Math. 2011.-v.1, no. 4, p.43-51.

25. Kopytko B., Shevchuk R. An inhomogeneous diffusion process model on a half-line with general boundary condition of Feller-Wentzel // Carpathian Mathematical Publikations, Vol.3, no. 2 (2011), 88-89.

26. Yu. V. Zhernovyj and B.I. Kopytko, Optimal Synthesis Problems for Markovian Queueing Systems with Several Given Characteristics // ISSN 1064-2269, Journal of Communications Technology and Electronics. - 2011. - Vol. 56, no. 12. - p. 1609-1619.

27. Yu. V. Zhernovyj, B.I. Kopytko, Optimal synthesis problem for Markov serving systems with several characteristics which are given // Informational Processes, v. 11, no.3, 2011, pp. 315-329.

28. W. Babenko, B. Kopytko, I. Senyszcz. Dynamika indeksu rozwoju systemu bankowego Ukrainy w latach 1999 - 2010 // Zbiór prac naukowych. Lwowski Uniwersytet Narodowy imienia Iwana Franki, 2011. Wydanie 23, cz. 1. s. 38-43.

29. B.I. Kopytko, A.F. Novosyadlo. Analytical model of generalized diffusion process with membrane located on a curved surface // Visnyk Chernivtsi Univ. - 2011. Math. v.1, no.1-2, p. 64-75.

30. B. Kopytko, K. Zhernovyi. Optimization of parameters of service for the modified М/M/1/M and M/M/1 queueing systems // Visnyk Lviv Univ., Ser. Appl. Math. Inform. 2011. v. 17, p.
129-138.

31. P.P. Kononchuk, B.I. Kopytko, Operator semigroups that describe Feller process on a line pasted from two diffusion processes // Teor. Imovir. ta Matem. Statyst., v.84, 2011, p. 86-96.


Wybrane publikacje za okres 1979-2010: artykuły naukowe

1. Kopytko B.I., Mylyo O.Ya., Tsapowska Zh.Ya. A parabolic conjugation problem with general boundary condition and a conjugation condition of Wentzel type // Carpathian Mathematical Publications - 2010. - V. 2, no. 2. - P. 55-73.

2. Pavlo P. Kononchuk and Bohdan I.Kopytko, Diffusion processes on a half-line with Feller-Wentzel boundary condition that correspond to reflection and jumps // Theory of Stochastic Processes, vol.16(32),no.2, 2010, p. 69-76.

3. B. I. Kopytko and Zh. Ya. Tsapovs’ka, Initial boundary-value problem with Wentzel-type conjugation condition for a parabolic equation with discontinuous coefficients // Journal of Mathematical Sciences. - 2009. - Vol. 160, No. 3. - P. 283-295.

4. Bohdan I. Kopytko and Mykola I. Portenko, The problem of pasting together two diffusion processes and classical potentials // Theory of Stochastic Processes, vol. 15 (31), no. 2, 2009, pp. 126-139.

5. Bohdan I. Kopytko and Andriy F. Novocyadlo. The Brownian motion process with generalized diffusion matrix and drift vector // Theory of stochastic Processes, vol. 14 (30), no. 2, 2008, pp. 60-70.

6. B.I. Kopytko, Zh.Ya. Tsapowska. Initial boundary-value problem with conjugation condition of Wentzell type for parabolic equation with discontinuous coefficients // Mathematical methods and physical-mechanical fields - 2008. - 51, no. 1. - p. 7-16.

7. Pavlo Kononchuk, Bogdan Kopytko. About Feller semigroup that describes a diffusion process on a half-line with nonlocal boundary condition // Math. Bull., v. 4, 2007. - p. 134-143.

8. Bogdan I.Kopytko and Mykola I.Portenko. An example of a stochastic differential equation with the property of weak non-uniqueness of a solution. // Theory of Stochastic Processes. - 2006. - 12 (28), no. 1 - 2. - P. 68 - 76.

9. Bogdan I. Kopytko, Mykola I. Portenko. One more example of a diffusion process whose local characteristics do not determine uniquely its transition probability // Theory of Stochastic Processes. - 2005. - 11 (27), no.1-2. - p. 74-80.

10. Portenko M. I., Kopytko B. I. Example of a diffusion process which Kolmogorov local characteristics do not determine uniquely its probability of transition // Reports of the National Academy of Sciences of Ukraine. Mathematics. - 2005. - no. 5. - p. 26-32.

11. Bogdan I.Kopytko, Mykola I.Portenko. On a Multidimensional Brownian Motion with a Membrane Located on a Hyperplane and Acting in an Oblique Direction // Ukrainian Mathematical Congress 2001. Probability Theory and Mathematical Statistics. Section 9. Proceedings. Kyiv, 2002, pp. 73-85.

12. Kopytko B.I., Tsapowska Zh.Ya. Potential method in parabolic boundary-value problem with Wentzell boundary condition // Visnyk Lviv Univ. Ser. Mech.-Math., 2000, v.56, p.106 - 115.

13. Kopytko B.I. An application of the Potential Method to construction of Diffusion Process in a Domain with the Wentsel boundary Condition // Theor. Probability and Math. Statist. No. 59, 1999, pp. 93 -100.

14. Bogdan I.Kopytko, Zhanna J.Tsapovska. Diffusion processes with discontinuous local characteristics of the movement. // Theory of Stochastic Processes, v.4(20), no. 1-2, 1998, pp.139-146.

15. Kopytko B.I. Operator semigroups describing the diffusion process in a domain with general boundary conditions // Reports of the National Academy of Sciences of Ukraine. Mathematics.- 1995.- no. 9.- p.15-18.

16. Kopytko B.I. Parabolic equation with discontinuous coefficients and generalized diffusion processes // Theory of Stochastic Processes, v. 1 (17), no.1. Kyiv, 1995, p.45-55.

17. Kopytko B.I. Construction of the diffusion process with generalized drift vector by means of solution some conjugation problem for the second-order parabolic type eqyation // Random Oper. Stoch. Egs., 1994. - 2. - no. 1. p.33-38.

18. Kopytko B.I. Continuous Markov processes pasted from two Wiener processes on a hyperplane admitting of a generalized drift vector and a generalized diffusion matrix // Asymptotic analysis of random evolutions. - Kyiv: Institute of Mathematics of the NAS of Ukraine. - 1994.- p.152-167.

19. Kopytko B.I. Semigroups of operators describing a multidimensional diffusion with partly reflecting borrier on a hyperplane // Random Oper. Stoch. Egs., 1992. - 1. - no. 1, p.95-102.

20. Kopytko B.I. Method of heat potentials in the problem of pasting together two diffusion processes // Reports of the National Academy of Sciences of Ukraine. Mathematics. - 1992. - no.12. - p.9-11.

21. Kopytko B.I. Multidimensional diffusion processes with partially reflecting boundary on a hyperplane // Matematychni Studii. Proceedings of the Lviv Mathematical Society. - 1992. v.1. - p.81-88.

22. Kopytko B.I. Diffusion processes with generalized drift vector and diffusion matrix // Probability theory and mathematical statistics. - Proceedings of the 6-th USSR Japan Symposium, Kiev; August 5-10, 1991. World Scientific. Singapore, 1992. - p.169-175.

23. Kopytko B.I. Űber das Verknűpfen zweier Difffusionsprocesse mit konstanten Diffusionmatrizen an einer Hyperebene // Mathematical Reseach. Stochastic Processes and Related Topic. - Akademiе-Verlag Berlin, 1991. - v.61. - p.75-79.

24. Kopytko B.I. Operator semigroups describing a generalized diffusion in a finite-dimensional Euclidean space // Stochastic analysis and its applications. - Kyiv: Mathematical Institute of the USSR Academy of Sciences. - 1989. - p.70-78.

25. Kopytko B.I. Generalized diffusion on a plane // Some problems of the modern theory of stochastic processes. - Kyiv: Mathematical Institute of the USSR Academy of Sciences. - 1988. - p.70-78.

26. Kopytko B.I., Portenko N.I. Analitical Methods of Pasting Together of Diffusion Processes // Lekture Notes in Matematics, 1021, 1983. - p.320-326. Springer-Verlag, Berlin, Heidenberg, New Jork, Tokyo.

27. Kopytko B.I. On pasting together two inhomogeneous diffusion processes on a line // Ukrainian Mathematical. Journal, - 1983. - v. 35, no.2. - p.156-163.

28. Kopytko B.I., Portenko N.I. Remarks on processes pasted from two Brownian motions // Some problems of the theory of stochastic processes. - Kyiv: Mathematical Institute of the USSR Academy of Sciences. - 1982. - p.67-79.

29. Balinskyi A.I., Kopytko B.I. On the conditions of the root of polynomial situation inside the unit disk // Mathematical methods and physical-mechanical fields. - Kyiv: 1980, v. 10, - p.11-15.

30. Kopytko B.I. On pasting together two Brownian motions // Random processes in problems of mathematical physics. - Kyiv: Mathematical Institute of the USSR Academy of Sciences. - 1979. - p.94-106.

Wybrane publikacje materiałów z konferencji naukowych:

1. Bohdan Kopytko, Roman Shevchuk, Diffusion in media with membranes and some nonlocal parabolic problems // International Conference “Stochastic Equations, Limit Theorems and Statistics of Stochastic Processes” dedicated to the 100th anniversary of I. I. Gikhman, September 17-22 2018, Kyiv, Ukraine. Abstracts, s. 46 - 47.

2. Bohdan Kopytko, Roman Shevchuk, On one class of nonlocal parabolic conjugation problems in the theory of diffusion processes with membranes // 10th Conference “Mathematical Modelling in Physics and Engineering” (MMPE” 2018), 18-21 June 2018, Czeęstochowa- Poraj, Poland. Conference Materials, s. 22 - 23.

3. Bohdan Kopytko, Roman Shevchuk, On two – parameter Feller semigroup with nonlocal condition for one – dimensional diffusion process // IX Conference “Mathematical Modelling in Physics and Engineering” (MMFT 2017), September, 18-21, 2017, Czeęstochowa- Poraj, Poland. Conference Materials, s. 75 - 76.

4. Bohdan Kopytko, Roman Shevchuk, The integral representation of Feller semigroup associated with diffusion processes a line with movable membrane, VII Conference "Mathematical Modelling in Physics and Engineering", June 23-25, 2016, Czestochowa-Hucisko, Poland. Conference Materials, p. 33.

5. B. I. Kopytko and R. V. Shevchuk, On one-dimensional processes with membranes, International Conference "Stochastic Processes in Abstract Spaces" dedicated to the 80th anniversary of Professor A. Ya. Dorogovtsev, 14-16 October, 2015, Kyiv, Ukraine. Program. Abstracts, p. 27.

6. Bohdan Kopytko, Zhanneta Tsapovska, Initial boundary value problems for the second order parabolic equation with the Wentzell type boundary and conjugation conditions, International V. Skorobohatko Mathematical Conference (August 25-28, 2015, Drohobycz, Ukraine). Abstracts, p.80.

7. Bohdan Kopytko, Roman Shevchuk, Generalized diffusion processes on a line with discontinuous local characteristics and sample paths, VII Conference "Mathematical Modelling in Physics and Technology", June 25-27, 2015, Czestochowa-Hucisko, Poland. Conference Materials, p. 33-34.

8. B. I. Kopytko, R. V. Shevchuk, On Feller semigroups associated with one-dimensional inhomogeneous diffusion processes with membranes. Taras Shevchenko National University of Kyiv International conference "Probability, reliability and stochastic optimization" dedicated to the 90th anniversary of V. S. Koroliuk, 80th anniversary of I. M. Kovalenko, 75th anniversary of P. S. Knopov and 75th anniversary of Yu. V. Kozachenko, April 7-10, 2015, Kyiv, Ukraine. Conference Materials, p. 54.

9. B.I. Kopytko, A.F. Novosyadlo, On pasting together multidimensional Brownian motions. All-Ukrainian scientific conference "Modern problems of probability theory and mathematical analysis", February 25 - March 3, 2013, Vorohta: Abstracts. - Ivano-Frankivsk, 2013. - p. 15-16.

10. Mykola Portenko and Bohdan Kopytko, Some mathematical models for the phenomenon of diffusion, International Conference dedicated to the 120th anniversary of Stefan Banach. Abstracts of Reports, Lviv, Ukraine, 17-21 September 2012, p. 275.

11. S. Huran, B. Kopytko, On some problems for second-order parabolic equations with a time derivative in conjugation condition. International V.Ya. Skorobohatko Mathematical Conference (September 19-23, 2011, Drohobych, Ukraine). - Abstracts. Lviv - 2011, p.60.

12. Kopytko B., Kononchuk P. Diffusion Processes with semitransparent Membrane on a Hypersurface with possible Break of a Traectory // Stochastic Analysis and random Dynamics. International Conference. June 14 - 20, 2009 Lviv, Ukraine. Abstracts, p. 116.

13. Kopytko B., Portenko M. The Problem of pasting Together two diffusion Processes and classical Potentials // Stochastic Analysis and random Dynamics. International Conference. June 14 - 20, 2009 Lviv, Ukraine. Abstracts, p. 117.

14. Kopytko B.I. On analytical methods in the theory of diffusion processes // Conference "Modern Problems in Probability Theory and Related Questions" dedicated to 90-th birth anniversary of I.I.Gichman. - Donetsk, 2008. - p. 36.

15. Serhiy Huran, Bohdan Kopytko. Classical solvability of the initial boundary-value problem for parabolic equation with a time derivative in conjugation condition. International V.Ya. Skorobohatko Mathematical Conference (September 24-28, 2007, Drohobych, Ukraine). - Abstracts. Lviv - 2007, p.82.

16. Bohdan Kopytko, Andriy Novocyadlo. Multidimentional diffusion processes with partial reflections on a fixed hyperplane that permit generalized drift vector and diffision matrix // International Conference: "Skorochod Space. 50 years on". 17-23 June, 2007, Kyiv, Ukraine. - Abstracts, Part 1, p.60.

17. Bogdan Kopytko and Zhanneta Tsapovska. Wentzell initial boundary-value problem for parabolic equation with discontinuous coefficients // International Conference on Differential Equations dedicated to the 100th anniversary of Ya. B. Lopatynsky, Lviv, September 12-17, 2006. Book of Abstracts. Lviv - 2006, p.36-37.

18. Mykola Portenko, Bohdan Kopytko. Integral representation of the semigroup of operators which describes the diffusion process with piecewise - continuous matrix of diffusion and generalized transfer vector concentrated on a surface // International Conference Modern Stochastics: Theory and Applications. Dedicated to the 60th anniversary of the Department of Probability Theory and Mathematical Statistics and to the memory of Professor M.Y.Yadrenko (1932-2004). Conference Materials. June 19-23, 2006, Kyiv, 2006, p.222.

19. Kopytko B.I., Portenko M.I. One example of a stochastic differential equation with the Property of weak nonuniquenes of a Solution // International Conference modern Problems and new Trends in Probability Theory. - Abstracts, I. - Chernivtsi, Ukraine. June 19-26, 2005. - p. 124 - 125.

20. Bogdan Kopytko, Zhanetta Tsapovska. Diffusion processes in medium with membrane which properties are described by the general Wentzell boundary condition // International Conference dedicated to the memory of V.Ya. Bunyakovskyi (1804-1889) (Kyiv, August 16-21, 2004). - Abstracts. - p.77-78.

21. B.I.Kopytko, Zh. Ja. Tsapovs'ka. Analytical method for constructing a diffusion process with generalized drift vector localized on a hypersurface.// International Conference on Functional Analysis and its Applications. Dedicated to the anniversary of Stefan Banach. Book of Abstracts. May 28-31, 2002, Lviv, Ukraine, pp. 113-114.

22. B.I. Kopytko, M.I. Portenko. On multidimensional Wiener process with a membrane which is located on a given hyperplane and acts along an oblique direction // Ukr. Math. Congress dedicated to 200-th birth anniversary of M.V. Ostrogratskyi. Kyiv. August, 21-23, 2001. Section 9: "Probability theory and mathematical statistics", p.17-18.

23. B. Kopytko , M.Portenko. On a Multidimensional Brownian Motion with a Membrane on a Hyperplane that acts along an Oblique Direction //The Internatonal Conference "Stochastic Analysis and its Applications", 10-17 Yune, Lviv, Ukraine. Abstracts of Comunications, Lviv-2001 ,p.62.

24. B.I.Kopytko and Zh.Ya.Tsapowska, Integral representation of a semigroup that describes a diffusion process in domain with Wentzel boundary condition // The Third Ukrainian - Scandinavian Conference in Probability Theory and Mathematical Statistics, June 8 - 12, 1999, Kyiv, Ukraine: Abstracts, p.64.

25. Bohdan Kopytko. On pasting together two diffusion processes on a hyperplane with a delay property // International conference on Modern Problems of Mechanics and Mathematics dedicated to 70-th birth anniversary of Yaroslav Stepanovych Pidstryhach and 25-anniversary of the Institute of Applied Problems of Mechanics and Mathematics NASU founded by him (May 25-28, 1998). Conference Proceedings. - Lviv: 1998. - p. 241.

26. Bohdan Kopytko. Analytic representation of operator semigroup desribing general diffusions in finite-dimensional euclidean spase // Stochastic dynamical systems: theory and applications. First Ukrainian-Scandinavian conference, Uzgorod, Ukraine, September 30 - Oktober 6: Abstracts. TBIMC Sciehtific Publishers, Kiev, 1995.- p. 35.

27. Kopytko B.I.. Method of parabolic potential theory in the problem of pasting together two diffusion processes // International mathematical conference dedicated to the memory of Hans Hahn (October 10-15, 1994, Chernivtsi). Abstracts. Chernivtsi: - 1994. - p.73.

28. Kopytko B.I., Portenko N.I. On analitic Methods of gluing of Diffusion Processes // IY Soviet - Japan. Sympos. on Theory of Prob. and Math. Statist. Tbilisi, August 23-29, 1982, Abstracrts, v. 2, p.33-34.

Wybrane publikacje książkowe:

1. Kopych I.M., Kopytko B.I., Sorokivskyy V.M., Babenko V.V., Stefanyak V.I., Applied Mathematical Statistics for Economists [text]: Manual: Lviv, The New World-2000, 2012 .-408p.

2. Kopytko B.I., Milyo O.Ya., Tsapovska Zh.Ya. Higher Mathematics. Elements of linear algebra and analytical geometry. Lecture texts.- Lviv: Ivan Franko National University, 2011.-301p.

3. Kopych I.M., Kopytko B.I., Sorokivskyi V.M., Babenko V.V., Stefanyak V.I. Probability Theory for Economists: Manual. - Lviv: LKA, 2008. - 351 p.

4. Bobyk O.I., Beregova G.I., Kopytko B.I. Theory of Probability and Mathematical Statistics - Manual. - Kyiv.: Professional, 2007. - 560 p.

5. Bobyk O.I., Berehova G.I., Kopytko B.I. Probability theory and mathematical statistics: Manual. - Lviv: LBI NBU , 2003. - 326 p.
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