Dmytro Gusak

• Doctor of Sciences in Mathematics from Institute of Mathematics. 1982.
  
• Candidate of Sciences in Mathematics (Ph.D.) from Institute of Mathematics, Ukraine. 1965. Kyiv University. Specialty: Theory of Probability and Mathematical Statistics.
  

• Leading scientific researcher at Institute of Mathematics of National Academy of Science of Ukraine
  

• Analytic methods in study of homogeneous process with independent increments.
  
• Boundary problems for homogeneous processes and random walks on Markov chain.
  
• Oscillating random walks and processes.
  
• Random walks on the superpositions of two renewal processes.
  
• Boundary problems for Risk processes.
  

Publications

Textbooks and tutorials

• Gusak, D.; Kukush, A.; Kulik, A.; Mishura, Y.; Pilipenko, A. Theory of stochastic processes. With applications to financial mathematics and risk theory.. - 380 pages. - Problem Books in Mathematics. New York, NY: Springer (ISBN 978-0-387-87861-4)., - 2010
• Gusak, D. V. Boundary value problems for processes with independent increments in the risk theory. ({\cyr Granichni1 zadachi1 dlya protsesi1v z nezalezhnimi prirostami v teoriï riziku}.). - 460 pages. - Pratsi Instytutu Matematyky Natsional’noï Akademiï Nauk Ukraïny. Matematyka ta ïï Zastosuvannya 65. Kyïv: Instytut Matematyky NAN Ukraïny (ISBN 978-966-02-4349-1)., - 2007
• Gusak, D.V. Boundary problems for processes with independent increments on Markov chains and for semi-Markov processes. (Granychni zadachi dlya protsesiv z nezalezhnymy pryrostamy na skinchennykh lantsyugakh Markova ta dlya napivmarkovs’kykh protsesiv.). - 320 pages. - Trudy Instytutu Matematyky Natsional’noï Akademiï Nauk Ukraïny. 18. Kyïv: Instytut Matematyky NAN Ukraïny., - 1998
• Bratijchuk, N.S.; Gusak, D.V. Boundary problems for processes with independent increments. (Granichnye zadachi dlya protsessov s nezavisimymi prirashcheniyami.). - 264 pages. - Kiev: Naukova Dumka., - 1990

Articles

• Gusak, Dmytro On some characteristics of the claim surplus process.. Theory Stoch. Process. 14(30), No. 1 - pages 49-59 - 2008
• Gusak, D.V. Boundary value problems for processes with independent increments in the risk theory.. Gusak, D. V., {\cyr Granichni1 zadachi1 dlya protsesi1v z nezalezhnimi prirostami v teoriï riziku}. Kyïv: Instytut Matematyky NAN Ukraïny (ISBN 978-966-02-4349-1). Pratsi Instytutu Matematyky Natsional’noï Akademiï Nauk Ukraïny. Matematyka ta ïï Zastosuvannya 65 - pages 1-460 - 2007
• Gusak, D.V. Behavior of classical risk processes after ruin and a multivariate ruin function.. Ukr. Mat. Zh. 59, No. 10 - pages 1339-1352 - 2007
• Gusak, D.V. Behavior of risk processes with random premiums after ruin and a multivariate ruin function.. Ukr. Mat. Zh. 59, No. 11 - pages 1473-1484 - 2007
• Gusak, D.V.; Karnaukh, E.V. Matrix factorization identity for almost semi-continuous processes on a Markov chain.. Theory Stoch. Process. 11, No. 27, Part 1-2 - pages 40-47 - 2005
• Gusak, D.V.; Karnaukh, E.V. On the exit from a finite interval for the risk processes with stochastic premiums.. Theory Stoch. Process. 11, No. 27, Part 3-4 - pages 71-81 - 2005
• Gusak, Dmytro V. Risk processes with stochastic premiums and distributions of their functionals.. Theory Stoch. Process. 11, No. 27, Part 1-2 - pages 29-39 - 2005
• Gusak, D.V. On the exit of one class of random walks from an interval.. Ukr. Mat. Zh. 57, No. 9 - pages 1209-1217 - 2005
• Gusak, Dmytro V. The connection of distributions of extrema for Lévy processes with its ladder points.. Theory Stoch. Process. 10(26), No. 3-4 - pages 35-42 - 2004
• STMAZ 1097.60029 Gusak, D.V. Versions of a compound Poisson process.. Teor. Jmovirn. Mat. Stat. 69 - pages 26-37 - 2004
• Gusak, D.V. Distributions of maximum of the Lévy processes and their relations with ladder points.. Nauk. Visn. Uzhgorod. Univ., Ser. Mat. 8 - pages 43-57 - 2003
• Gusak, D.V. Jump-over functionals for integer-valued Poisson processes.. Teor. Jmovirn. Mat. Stat. 68 - pages 24-36 - 2003
• Gusak, Oleg; Dayar, Tuğrul; Fourneau, Jean-Michel Lumpable continuous-time stochastic automata networks.. Eur. J. Oper. Res. 148, No. 2 - pages 436-451 - 2003
• Gusak, D.V. Compound Poisson processes with two-sided reflection.. Ukr. Mat. Zh. 54, No.12 - pages 1616-1625 - 2002
• Gusak, D.V. Distribution of overjump functionals of a semicontinuous homogeneous process with independent increments.. Ukr. Math. J. 54, No.3 - pages 371-397 - 2002
• Gusak, D.V. On the distribution of overjumping functionals of homogeneous process with independent increments.. Nauk. Visn. Uzhgorod. Univ., Ser. Mat. 6 - pages 47-65 - 2001
• Gusak, D.V. Factorization identity for semicontinuous process defined on a Markov chain. . Theory Probab. Math. Stat. 64 - pages 37-50 - 2001
• Gusak, Dmytro The distribution of extrema for risk processes on the finite Markov chain.. Theory Stoch. Process. 7(23), No.1-2 - pages 109-120 - 2001
• Gusak, D.V.; Bratijchuk, M.S.; Svishchuk, A.V. On the creative contribution of V. S. Korolyuk to the development of probability theory.. Ukr. Math. J. 52, No.8 - pages 1161-1178 - 2000
• Gusak, D.V. Ruin problem for an inhomogeneous semicontinuous integer-valued process.. Ukr. Math. J. 52, No.2 - pages 234-248 - 2000
• Samojlenko, A.M.; Skorokhod, A.V.; Kovalenko, I.M.; Yadrenko, M.I.; Gusak, D.V. Vladimir Semenovich Korolyuk (on his 75th birthday).. Ukr. Math. J. 52, No.8 - pages 1159-1160 - 2000
• Gusak, Dmytro V. The ruin problems for nonhomogeneous semicontinuous integer-valued processes.. Theory Stoch. Process. 5(21), No.3-4 - pages 72-83 - 1999
• Gusak, D.V.; Korkuna, O.P. On a moment of the first passage of a level by oscillatory semicontinuous processes.. Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 1999, No.11 - pages 18-23 - 1999
• Gusak, D.V. Limit behavior of the distribution of the ruin moment of a modified risk process.. Ukr. Math. J. 51, No.6 - pages 948-955 - 1999
• Gusak, D.V. On a generalized semicontinuous integer-valued Poisson process with reflection.. Theory Probab. Math. Stat. 59 - pages 41-46 - 1999
• Gusak, D.V. On the first ruin moment for a modified risk process with immediate reflection.. Ukr. Math. J. 50, No.10 - pages 1622-1629 - 1998
• Gusak, D.V. On modifications of ruin processes.. Theory Probab. Math. Stat. 56 - pages 87-95 - 1998
• Gusak, Dmytro V. On the modified risk process with reflection.. Theory Stoch. Process. 3(19), No.1-2 - pages 197-207 - 1997
• Gusak, D.V. Basic identities for additive continuously distributed sequences.. Ukr. Math. J. 48, No.12 - pages 1868-1879 - 1996
• Gusak, D.V. A sojourn time in a fixed state for integer valued random additive sequences.. Dopov. Akad. Nauk Ukr. 1996, No.2 - pages 16-20 - 1996
• Gusak, D.V. The joint distribution of a process defined by the sum of a random number of summands and its extrema. I.. Theory Probab. Math. Stat. 52 - pages 43-54 - 1996
• Gusak, D.V. On crossing of a level by process defined by sums of a random number of terms.. Ukr. Math. J. 47, No.7 - pages 1030-1049 - 1995
• Gusak, D.V. Fundamental identities for boundary functionals of additive sequences.. Exploring Stochastic Laws - pages 135-146 - 1995
• Gusak, D.V.; Rozumenko, A.M. On extrema of integer-valued processes, defined by sums of a random number of addenda.. Random Operators \& Stoch. Equat. 3 - pages 87-100 - 1995
• Gusak, D.V. On crossing of a level by process defined by sums of a random number of terms.. Ukr. Math. J. 47, No.7 - pages 1030-1049 - 1995
• Gusak, D.V. Fundamental identities for boundary functionals of additive sequences.. Skorokhod, A. V. (ed.) et al., Exploring stochastic laws. Festschrift in honour of the 70th birthday of Academician Vladimir Semenovich Korolyuk. Utrecht: VSP - pages 135-146 - 1995
• Gusak, D.V. The ruin probability and the first exit time for a class of processes with independent increments. . 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 - pages 329-340 - 1995
• Gusak, D.V.; Rozumenko, A.M. On extrema of integer-valued processes, defined by sums of a random number of addenda.. Random Oper. Stoch. Equ. 3, No.1 - pages 87-100 - 1995
• Gusak, D.V. Oscillating processes with independent increments and nondegenerate Wiener component.. Ukr. Math. J. 42, No.10 - pages 1257-1261 - 1990
• Gusak, D.V. On oscillating random walk schemes. II.. Theory Probab. Math. Stat. 40 - pages 11-17 - 1990
• Gusak, D.V.; Korkuna, O.P. Semicontinuous oscillating walks with the nondegenerate Wiener component.. Korolyuk, V. S. (ed.), Asymptotic and applied problems in the theory of random evolutions. Collection of scientific works. Kiev: Institut Matematiki AN USSR. - pages 7-12 - 1990
• Gusak, D.V. On oscillating random walk schemes. I.. Theory Probab. Math. Stat. 39 - pages 41-46 - 1989
• Gusak, D.V. Boundary value problems for processes with independent increments and cumulants of a special form.. Analytical methods for the investigation of the evolution of stochastic systems, Collect. Sci. Works, Kiev - pages 4-10 - 1989
• Gusak, D.V.; Tureniyazova, A.I. On the Poisson lattice-type semicontinuous processes on the Markov chain.. Ukr. Mat. J. 39 - pages 707-711 - 1988
• Gusak, D.V. On a model of oscillating random walk.. Analytical methods in probabilistic problems, Collect. Sci. Works - pages 25-27 - 1988
• Gusak, D.V. On oscillating schemes of a random walk. I.. Teor. Veroyatn. Mat. Stat. 39 - pages 33-39 - 1988
• Gusak, D.V.; Tureniyazova, A.I. Lattice semicontinuous Poisson processes on Markov chains.. Ukr. Math. J. 39, No.6 - pages 573-576 - 1987
• Gusak, D.V.; Tureniyazova, A.I. On lattice semicontinuous Poisson processes on a Markov chain.. Ukr. Mat. Zh. 39, No.6 - pages 707-711 - 1987
• Gusak, D.V. On a modification of the oscillating random walk.. Application of analytical methods to probability problems, Collect. sci. Works, Kiev 1986 - pages 16-27 - 1986
• Bratijchuk, N.S.; Gusak, D.V. Ergodic distribution of an oscillating process with independent increments.. Ukr. Math. J. 38 - pages 465-471 - 1986
• Kaplan, B.I.; Gusak, D.V. An asymptotic representation of the potential of a lower continuous random walk on a Markov chain. . Analytical methods in reliability theory, Collect. sci. Works, Kiev 1985 - pages 70-75 - 1985
• Gusak, D.V.; Kaplan, B.Iv. On the distribution of the time of stay in a fixed state for a scheme of walks with discretely distributed jumps.. Analytical methods in problems of probability theory, Collect. sci. Works, Kiev 1984 - pages 27-40 - 1984
• Gusak, D.V. Distribution of the sojourn time of a homogeneous process with independent increments over an arbitrary level.. Theory Probab. Appl. 28 - pages 503-514 - 1984
• Gusak, D.V. On the time of staying over a level for a homogeneous process with independent increments defined on a Markov chain.. Application of analytical methods in probability theory, Collect. sci. Works, Kiev 1983 - pages 34-41 - 1983
• Gusak, D.V. The distribution of the sojourn time of the homogeneous process with independent increments above an arbitrary level.. Teor. Veroyatn. Primen. 28, No.3 - pages 478-503 - 1983
• Gusak, D.V. How often is the sum of independent random variables larger than a given number?. Ukr. Math. J. 34 - pages 234-239 - 1983
• Gusak, D.V. Factorized identities for sums of a random number of summands.. Applied problems of probability theory, Collect. sci. Works, Kiev 1982 - pages 25-44 - 1982
• Gusak, D.V. On the stay above the level of a sum of independent random variables.. Ukr. Mat. Zh. 34 - pages 289-295 - 1982
• Gusak, D.V.; Elejko, O.I. On an oscillating Poisson process.. Analytical methods of investigation in probability theory, Collect. sci. Works, Kiev 1981 - pages 35-47 - 1981
• Gusak, D.V. On boundary functionals for sums of a random number of summands.. Analytical methods of investigation in probability theory, Collect. sci. Works, Kiev 1981 - pages 20-35 - 1981
• Gusak, D.V. The distribution of the time of staying above an arbitrary level for a homogeneous process with indendent increments.. Dopov. Akad. Nauk Ukr. RSR, Ser. A 1981, No.1 - pages 14-16 - 1981
• Gusak, D.V. Intersection of a level by a homogeneous process with independent increments and a nondegenerate Wiener component.. Ukr. Math. J. 32 - pages 247-250 - 1981
• Gusak, D.V. Remark to the paper "On the compound Poisson process on a Markov chain".. Theory Probab. Math. Stat. 21 - pages 43-45 - 1980
• Gusak, D.V. On the level-crossing from homogeneous processes with independent increments and non-degenerative Wiener component.. Ukr. Mat. Zh. 32 - pages 373-378 - 1980
• Gusak, D.V. On the compound Poisson process on a Markov chain.. Theory Probab. Math. Stat. 17 - pages 45-54 - 1979
• Gusak, D.V. A distribution of limit overleap value for compound Poisson processes on a Markov chain.. Analytical Methods in probability theory, Collect. Sci. Works, Kiev 1979 - pages 34-43 - 1979
• Gusak, D.V. Remark to the article "On compound Poisson process on a Markov chain".. Teor. Veroyatn. Mat. Stat. 21 - pages 39-42 - 1979
• Gusak, D.V. On continuous homogeneous processes with independent increments on a Markov chain.. Theory Probab. Math. Stat. 16 - pages 29-46 - 1978
• Gusak, D.V.; Peresypkina, S.I. The time spent above a fixed level by a class of controlled random processes.. Ukr. Math. J. 30 - pages 270-274 - 1978
• Gusak, D.V. The distribution of the time the maximum is achieved by a homogeneous process with independent increments.. Select. Translat. Math. Stat. Probab. 14 - pages 107-110 - 1978
• Gusak, D.V.; Peresypkina, S.I. Über die Aufenthaltszeit oberhalb eines Niveau einer Klasse regelbarer stochastischer Prozesse.. Ukr. Mat. Zh. 30 - pages 352-357 - 1978
• Gusak, D.V. On compound Poisson process on a Markov chain.. Teor. Veroyatn. Mat. Stat. 17 - pages 41-51 - 1977
• Gusak, D.V. On continuous homogeneous processes with independent increments on a Markov chain.. Teor. Veroyatn. Mat. Stat. 16 - pages 29-45 - 1977
• Gusak, D.V. Probabilities of the first exit for continuous processes with independent increments on a Markov chain. . Proc. 3rd Japan-USSR Symp. Probab. Theory, Taschkent 1975, Lect. Notes Math. 550 - pages 181-193 - 1976
• Gusak, D.V.; Korolyuk, V.S. The asymptotic behavior of semi-Markov processes with a decomposable set of states.. Theor. Probab. math. Statist. 5 - pages 43-51 - 1976
• Gusak, D.V. A remark on canonical and infinitely divisible factorization.. Theor. Probab. math. Statist. 4 - pages 51-53 - 1976
• Gusak, D.V. Extreme values of nondegenerate Wiener processes controlled by a finite Markov chain.. Theor. Probab. math. Statist. 6 - pages 47-52 - 1976
• Mitropol’skij, Yu.A.; Skorokhod, A.V.; Gusak, D.V.; Turbin, A.F. Asymptotic method for probability problems.. Ukr. Math. J. 27 - pages 380-384 - 1976
• Mitropol’skij, Yu.A.; Skorokhod, A.V.; Gusak, D.V.; Turbin, A.F. Asymptotic methods in probability problems.. Ukr. Mat. Zh. 27 - pages 471-476 - 1975
• Gusak, D. V. A class of processes with independent increments on a finite Markov chain.. Ukr. Math. J. 25 - pages 139-145 - 1974
• Gusak, D.V.; Peresypkina, S.I. Distribution of the exit time and value for homogeneous processes with independent increments given on a finite Markov chain.. Ukr. Math. J. 26 - pages 239-245 - 1974
• Gusak, D.V.; Peresypkina, S.I. On the moment of reaching the maximum for homogeneous processes with independent increments controlled by a Markov chain.. Dopov. Akad. Nauk Ukr. RSR, Ser. A 1974 - pages 589-592 - 1974
• Gusak, D.V.; Korolyuk, V.S. The distribution of functionals of homogeneous processes with independent increments.. Theor. Probab. math. Statist. 1 - pages 53-72 - 1974
• Gusak, D.V. Über eine Klasse von Prozessen mit unabhängigen Zuwächsen auf einer endlichen Markovschen Kette. . Ukr. Mat. Zh. 25 - pages 170-178 - 1973
• Gusak, D.V. Verteilung der Extrema von Wiener-Prozessen mit Verschiebung, die durch endliche Markovsche Ketten gesteuert werden.. Inform. Theory, statist. Decision Funct., Random Processes; Transact. 6th Prague Conf. - pages 207-212 - 1973
• Gusak, D.V. On the continuous passage through a fixed level of a homogeneous process with independent increments on a Markov chain.. Proc. 2nd Japan-USSR Sympos. Probab. Theory, Kyoto 1972, Lect. Notes Math. 330 - pages 95-103 - 1973
• Gusak, D.V. Extremalwerte nichtausgearteter Wienerscher Prozesse, die von einer endlichen Markovschen Kette gesteuert werden.. Teor. Veroyatn. Mat. Stat. 6 - pages 49-53 - 1972
• Gusak, D.V.; Korolyuk, V.S. The asymptotic behaviour of semi-Markov processes with a decomposable set of states.. Teor. Veroyatn. Mat. Stat. 5 - pages 43-50 - 1971
• Gusak, D.V. Random walk described by a homogeneous process with independent increments, and asymptotic analysis of its characteristics.. Select. Translat. Math. Statist. Probab. 9 - pages 189-203 - 1971
• Gusak, D.V. A remark on a canonical and infinitely divisible factorization.. Teor. Veroyatn. Mat. Stat. 4 - pages 58-60 - 1971
• Gusak, D.V.; Korolyuk, V.S. On the joint distribution of a process with stationary increments and its maximum.. Theor. Probab. Appl. 14 - pages 400-409 - 1970
• Gusak, D.V.; Korolyuk, V.S. Verteilung von Funktionalen inhomogener Prozesse mit unabhängigen Inkrementen.. Teor. Veroyatn. Mat. Stat. 1 - pages 55-73 - 1970
• Gusak, D.V. Über die Extremalwerte der von einer endlichen Markovschen Kette gesteuerten Wienerschen Prozesse.. Dopov. Akad. Nauk Ukr. RSR, Ser. A 1970 - pages 873-875 - 1970
• Gusak, D.V. On the joint distribution of the first exit time and exit value for homogeneous processes with independent increments.. Theor. Probab. Appl. 14 - pages 14-23 - 1969
• Gusak, D.V.; Korolyuk, V.S. On the joint distribution of a process with stationary increments and its maximum.. Teor. Veroyatn. Primen. 14 - pages 421-430 - 1969
• Gusak, D.V. On canonical and infinitely divisible factorization.. Dopov. Akad. Nauk Ukr. RSR, Ser. A 1969 - pages 294-298 - 1969
• Gusak, D.V. On the distribution of the moment of reaching the maximum by a homogeneous process with independent increments.. Dopov. Akad. Nauk Ukr. RSR, Ser. A 1968 - pages 396-399 - 1968
• Gusak, D.V.; Kooljuk, V.S. On the first passage time across a given level for processes with independent increments.. Theor. Probab. Appl. 13 - pages 448-456 - 1968
• Gusak, D.V. Eine Irrfahrt, die vermittels eines homogenen Prozesses mit unabhängigen Zuwächsen beschrieben wird, und die asymptotische Analyse ihrer Charakteristiken.. Ukr. Mat. Zh. 18, No.1 - pages 24-35 - 1966
• Gusak, D.V. Asymptotische Analyse in einem Gitterschema der Irrfahrt, die durch einen Prozeß mit unabhängigen Zuwächsen beschrieben wird.. Dopov. Akad. Nauk Ukr. RSR 1966 - pages 1243-1246 - 1966
• Korolyuk, V.S.; Gusak, D.V. The asymptotic behavior of distributions of maximal deviations in a Poisson process.. Select. Transl. Math. Stat. Probab. 5 - pages 270-277 - 1965
• Gusak, D.V. Zur Asymptotik der Verteilung der Zeit des ersten Austritts eines homogenen Prozesses mit unabhängigem Zuwachs.. Ukr. Mat. Zh. 16 - pages 463-474 - 1964
• Gusak, D.V. Zur Asymptotik der Verteilung der Extrema eines homogenen Prozesses mit unabhängigen Zuwächsen. . Tr. naucn. Konf. Inz., Aspirant. mladsih naucn. Sotrudn. Inst. Mat. AN USSR 1963 - pages 176-179 - 1963
• Gusak, D.V. On the asymptotic behaviour of the extremum distributionof a centered homogeneous process with independent increments.. Dopov. Akad. Nauk Ukr. RSR 1963 - pages 1287-1291 - 1963
• Korolyuk, V.S.; Gusak, D.V. Zur Asymptotik der Verteilungen der maximalen Abweichungen bei einem Poissonschen Prozeß.. Ukr. Mat. Zh. 14 - pages 138-144 - 1962