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.
  

Conferences

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.". Problem Books in Mathematics. New York, NY: Springer (ISBN 978-0-387-87861-4)., 380 p. - 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}.)". Pratsi Instytutu Matematyky Natsional’noï Akademiï Nauk Ukraïny. Matematyka ta ïï Zastosuvannya 65. Kyïv: Instytut Matematyky NAN Ukraïny (ISBN 978-966-02-4349-1)., 460 p. - 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.)". Trudy Instytutu Matematyky Natsional’noï Akademiï Nauk Ukraïny. 18. Kyïv: Instytut Matematyky NAN Ukraïny., 320 p. - 1998
• Bratijchuk, N.S.; Gusak, D.V. "Boundary problems for processes with independent increments. (Granichnye zadachi dlya protsessov s nezavisimymi prirashcheniyami.)". Kiev: Naukova Dumka., 264 p. - 1990

Articles

2008
• Gusak, Dmytro "On some characteristics of the claim surplus process.". Theory Stoch. Process. 14(30), No. 1, pp. 49 - 59, - 2008
2007
• 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, pp. 1 - 460, - 2007
• Gusak, D.V. "Behavior of classical risk processes after ruin and a multivariate ruin function.". Ukr. Mat. Zh. 59, No. 10, pp. 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, pp. 1473 - 1484, - 2007
2005
• 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, pp. 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, pp. 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, pp. 29 - 39, - 2005
• Gusak, D.V. "On the exit of one class of random walks from an interval.". Ukr. Mat. Zh. 57, No. 9, pp. 1209 - 1217, - 2005
2004
• Gusak, Dmytro V. "The connection of distributions of extrema for Lévy processes with its ladder points.". Theory Stoch. Process. 10(26), No. 3-4, pp. 35 - 42, - 2004
• STMAZ 1097.60029 Gusak, D.V. "Versions of a compound Poisson process.". Teor. Jmovirn. Mat. Stat. 69, pp. 26 - 37, - 2004
2003
• Gusak, D.V. "Distributions of maximum of the Lévy processes and their relations with ladder points.". Nauk. Visn. Uzhgorod. Univ., Ser. Mat. 8, pp. 43 - 57, - 2003
• Gusak, D.V. "Jump-over functionals for integer-valued Poisson processes.". Teor. Jmovirn. Mat. Stat. 68, pp. 24 - 36, - 2003
• Gusak, Oleg; Dayar, Tuğrul; Fourneau, Jean-Michel "Lumpable continuous-time stochastic automata networks.". Eur. J. Oper. Res. 148, No. 2, pp. 436 - 451, - 2003
2002
• Gusak, D.V. "Compound Poisson processes with two-sided reflection.". Ukr. Mat. Zh. 54, No.12, pp. 1616 - 1625, - 2002
• Gusak, D.V. "Distribution of overjump functionals of a semicontinuous homogeneous process with independent increments.". Ukr. Math. J. 54, No.3, pp. 371 - 397, - 2002
2001
• Gusak, D.V. "On the distribution of overjumping functionals of homogeneous process with independent increments.". Nauk. Visn. Uzhgorod. Univ., Ser. Mat. 6, pp. 47 - 65, - 2001
• Gusak, D.V. "Factorization identity for semicontinuous process defined on a Markov chain. ". Theory Probab. Math. Stat. 64, pp. 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, pp. 109 - 120, - 2001
2000
• 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, pp. 1161 - 1178, - 2000
• Gusak, D.V. "Ruin problem for an inhomogeneous semicontinuous integer-valued process.". Ukr. Math. J. 52, No.2, pp. 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, pp. 1159 - 1160, - 2000
1999
• Gusak, Dmytro V. "The ruin problems for nonhomogeneous semicontinuous integer-valued processes.". Theory Stoch. Process. 5(21), No.3-4, pp. 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, pp. 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, pp. 948 - 955, - 1999
• Gusak, D.V. "On a generalized semicontinuous integer-valued Poisson process with reflection.". Theory Probab. Math. Stat. 59, pp. 41 - 46, - 1999
1998
• Gusak, D.V. "On the first ruin moment for a modified risk process with immediate reflection.". Ukr. Math. J. 50, No.10, pp. 1622 - 1629, - 1998
• Gusak, D.V. "On modifications of ruin processes.". Theory Probab. Math. Stat. 56, pp. 87 - 95, - 1998
1997
• Gusak, Dmytro V. "On the modified risk process with reflection.". Theory Stoch. Process. 3(19), No.1-2, pp. 197 - 207, - 1997
1996
• Gusak, D.V. "Basic identities for additive continuously distributed sequences.". Ukr. Math. J. 48, No.12, pp. 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, pp. 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, pp. 43 - 54, - 1996
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, pp. 1030 - 1049, - 1995
• Gusak, D.V. "Fundamental identities for boundary functionals of additive sequences.". Exploring Stochastic Laws, pp. 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, pp. 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, pp. 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, pp. 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, pp. 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, pp. 87 - 100, - 1995
1990
• Gusak, D.V. "Oscillating processes with independent increments and nondegenerate Wiener component.". Ukr. Math. J. 42, No.10, pp. 1257 - 1261, - 1990
• Gusak, D.V. "On oscillating random walk schemes. II.". Theory Probab. Math. Stat. 40, pp. 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., pp. 7 - 12, - 1990
1989
• Gusak, D.V. "On oscillating random walk schemes. I.". Theory Probab. Math. Stat. 39, pp. 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, pp. 4 - 10, - 1989
1988
• Gusak, D.V.; Tureniyazova, A.I. "On the Poisson lattice-type semicontinuous processes on the Markov chain.". Ukr. Mat. J. 39, pp. 707 - 711, - 1988
• Gusak, D.V. "On a model of oscillating random walk.". Analytical methods in probabilistic problems, Collect. Sci. Works, pp. 25 - 27, - 1988
• Gusak, D.V. "On oscillating schemes of a random walk. I.". Teor. Veroyatn. Mat. Stat. 39, pp. 33 - 39, - 1988
1987
• Gusak, D.V.; Tureniyazova, A.I. "Lattice semicontinuous Poisson processes on Markov chains.". Ukr. Math. J. 39, No.6, pp. 573 - 576, - 1987
• Gusak, D.V.; Tureniyazova, A.I. "On lattice semicontinuous Poisson processes on a Markov chain.". Ukr. Mat. Zh. 39, No.6, pp. 707 - 711, - 1987
1986
• Gusak, D.V. "On a modification of the oscillating random walk.". Application of analytical methods to probability problems, Collect. sci. Works, Kiev 1986, pp. 16 - 27, - 1986
• Bratijchuk, N.S.; Gusak, D.V. "Ergodic distribution of an oscillating process with independent increments.". Ukr. Math. J. 38, pp. 465 - 471, - 1986
1985
• 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, pp. 70 - 75, - 1985
1984
• 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, pp. 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, pp. 503 - 514, - 1984
1983
• 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, pp. 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, pp. 478 - 503, - 1983
• Gusak, D.V. "How often is the sum of independent random variables larger than a given number?". Ukr. Math. J. 34, pp. 234 - 239, - 1983
1982
• Gusak, D.V. "Factorized identities for sums of a random number of summands.". Applied problems of probability theory, Collect. sci. Works, Kiev 1982, pp. 25 - 44, - 1982
• Gusak, D.V. "On the stay above the level of a sum of independent random variables.". Ukr. Mat. Zh. 34, pp. 289 - 295, - 1982
1981
• Gusak, D.V.; Elejko, O.I. "On an oscillating Poisson process.". Analytical methods of investigation in probability theory, Collect. sci. Works, Kiev 1981, pp. 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, pp. 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, pp. 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, pp. 247 - 250, - 1981
1980
• Gusak, D.V. "Remark to the paper "On the compound Poisson process on a Markov chain".". Theory Probab. Math. Stat. 21, pp. 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, pp. 373 - 378, - 1980
1979
• Gusak, D.V. "On the compound Poisson process on a Markov chain.". Theory Probab. Math. Stat. 17, pp. 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, pp. 34 - 43, - 1979
• Gusak, D.V. "Remark to the article "On compound Poisson process on a Markov chain".". Teor. Veroyatn. Mat. Stat. 21, pp. 39 - 42, - 1979
1978
• Gusak, D.V. "On continuous homogeneous processes with independent increments on a Markov chain.". Theory Probab. Math. Stat. 16, pp. 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, pp. 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, pp. 107 - 110, - 1978
• Gusak, D.V.; Peresypkina, S.I. "Über die Aufenthaltszeit oberhalb eines Niveau einer Klasse regelbarer stochastischer Prozesse.". Ukr. Mat. Zh. 30, pp. 352 - 357, - 1978
1977
• Gusak, D.V. "On compound Poisson process on a Markov chain.". Teor. Veroyatn. Mat. Stat. 17, pp. 41 - 51, - 1977
• Gusak, D.V. "On continuous homogeneous processes with independent increments on a Markov chain.". Teor. Veroyatn. Mat. Stat. 16, pp. 29 - 45, - 1977
1976
• 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, pp. 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, pp. 43 - 51, - 1976
• Gusak, D.V. "A remark on canonical and infinitely divisible factorization.". Theor. Probab. math. Statist. 4, pp. 51 - 53, - 1976
• Gusak, D.V. "Extreme values of nondegenerate Wiener processes controlled by a finite Markov chain.". Theor. Probab. math. Statist. 6, pp. 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, pp. 380 - 384, - 1976
1975
• Mitropol’skij, Yu.A.; Skorokhod, A.V.; Gusak, D.V.; Turbin, A.F. "Asymptotic methods in probability problems.". Ukr. Mat. Zh. 27, pp. 471 - 476, - 1975
1974
• Gusak, D. V. "A class of processes with independent increments on a finite Markov chain.". Ukr. Math. J. 25, pp. 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, pp. 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, pp. 589 - 592, - 1974
• Gusak, D.V.; Korolyuk, V.S. "The distribution of functionals of homogeneous processes with independent increments.". Theor. Probab. math. Statist. 1, pp. 53 - 72, - 1974
1973
• Gusak, D.V. "Über eine Klasse von Prozessen mit unabhängigen Zuwächsen auf einer endlichen Markovschen Kette. ". Ukr. Mat. Zh. 25, pp. 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., pp. 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, pp. 95 - 103, - 1973
1972
• Gusak, D.V. "Extremalwerte nichtausgearteter Wienerscher Prozesse, die von einer endlichen Markovschen Kette gesteuert werden.". Teor. Veroyatn. Mat. Stat. 6, pp. 49 - 53, - 1972
1971
• Gusak, D.V.; Korolyuk, V.S. "The asymptotic behaviour of semi-Markov processes with a decomposable set of states.". Teor. Veroyatn. Mat. Stat. 5, pp. 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, pp. 189 - 203, - 1971
• Gusak, D.V. "A remark on a canonical and infinitely divisible factorization.". Teor. Veroyatn. Mat. Stat. 4, pp. 58 - 60, - 1971
1970
• Gusak, D.V.; Korolyuk, V.S. "On the joint distribution of a process with stationary increments and its maximum.". Theor. Probab. Appl. 14, pp. 400 - 409, - 1970
• Gusak, D.V.; Korolyuk, V.S. "Verteilung von Funktionalen inhomogener Prozesse mit unabhängigen Inkrementen.". Teor. Veroyatn. Mat. Stat. 1, pp. 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, pp. 873 - 875, - 1970
1969
• 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, pp. 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, pp. 421 - 430, - 1969
• Gusak, D.V. "On canonical and infinitely divisible factorization.". Dopov. Akad. Nauk Ukr. RSR, Ser. A 1969, pp. 294 - 298, - 1969
1968
• 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, pp. 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, pp. 448 - 456, - 1968
1966
• 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, pp. 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, pp. 1243 - 1246, - 1966
1965
• Korolyuk, V.S.; Gusak, D.V. "The asymptotic behavior of distributions of maximal deviations in a Poisson process.". Select. Transl. Math. Stat. Probab. 5, pp. 270 - 277, - 1965
1964
• Gusak, D.V. "Zur Asymptotik der Verteilung der Zeit des ersten Austritts eines homogenen Prozesses mit unabhängigem Zuwachs.". Ukr. Mat. Zh. 16, pp. 463 - 474, - 1964
1963
• 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, pp. 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, pp. 1287 - 1291, - 1963
1962
• Korolyuk, V.S.; Gusak, D.V. "Zur Asymptotik der Verteilungen der maximalen Abweichungen bei einem Poissonschen Prozeß.". Ukr. Mat. Zh. 14, pp. 138 - 144, - 1962