Contacts   

Degrees

Employment

Management  and Administration

Membership in Scientific Organizations

Membership in Editorial Boards of Journals

Scientific Interests

Seminars organized

Supervision experience      

Awards and Grants     

Lectures at International Conferences

Participation in the Conference organizing

Publications

 

Publications

 

Books:

 

1.

Stokhasticheskiĭ analiz i sluchaĭnye otobrazheniya v gil’bertovom prostranstve  (Russian) [Stochastic analysis and random mappings in a Hilbert space] “Naukova Dumka”, Kiev, 1992. 120 pp. ISBN: 5-12-003154-4.

 

2.

Stochastic analysis and random maps in Hilbert space. English edition of the 1992 Russian original [“Naukova Dumka”, Kiev].  – VSP, Utrecht, 1994. – ii+109 pp. ISBN: 90-6764-163-4.

 

3.

Stokhasticheskie uravneniya s uprezhdeniem (Russian) [Anticipating stochastic equations] Trudi Īnstitutu Matematiki Natsīonal’noï Akademīï Nauk Ukraïni [Proceedings of the Institute of Mathematics of the National Academy of Sciences of the Ukraine], 15. Natsīonal’na Akademīya Nauk Ukraïni, Īnstitut Matematiki, Kiev, 1996. 152 pp. ISBN: 966-02-0019-6.

 

4.

Meroznachnye protsessy i stokhasticheskie potoki (Russian) [Measure-valued processes and stochastic flows] Pratsī Īnstitutu Matematiki Natsīonal’noï Akademīï Nauk Ukraïni. Matematika ta ïï Zastosuvannya [Proceedings of Institute of Mathematics of NAS of Ukraine. Mathematics and its Applications], 66. Natsīonal’na Akademīya Nauk Ukraïni, Īnstitut Matematiki, Kiev, 2007. 290 pp. ISBN: 978-966-02-4540-2.

 

5.

Lokal’nye vremena samoperesecheniya dlya gaussovskih protsessov (Russian) [Self-intersection local times for Gaussian processes]  LAP LAMBERT Academic Publishing, Saarbrücken, 2011. – 152 pp. ISBN: 978-3-8454-7735-0 (with Izyumtseva O.L.).

 

 

Papers:

 

1.

A property of the Radon-Nikodým derivative  (Russian) // Teor. Veroyatnost. i Mat. Statist. No. 28 (1983), P. 141–144.

2.

Notes on the Toeplitz theorem. (Russian)  // Mathematics today ‘83, 1983,       P. 175-180, "Vishcha Shkola'', Kiev.

3.

Convergence of quadratic forms of random elements in Banach algebra // Teor. Veroyatnost. i Mat. Statist., 1984. – No. 31. – P. 31-39   (Russian).

4.

On the one geometrical optimization problem // In the world of mathematics. – Kiev: Radianska Shkola, 1984. – P. 141-149. (Russian).

5.

Admissible multipliers for Gaussian measures in Hilbert algebra and in C ([0,1]) // Random processes. Theory and practice. – Kiev: Akad. Nauk Ukrain. SSR, Inst. Mat., Kiev, 1985. –- P. 42-48. (Russian).

6.

A characterization of Gaussian distribution in Banach space // Teor. Veroyatnost. i Mat. Statist., 1985,  No. 33. – P. 20-25. (Russian).

7.

A characteristic functional of the quadratic form of Gaussian elements in Hilbert algebra //  Ukrainian Math. J., 1986. – V.38, N 2. – P. 230-233.

8.

On a class of Gaussian random operators  // Probabilistic methods for the investigation of systems with an infinite number of degrees of freedom. – Kiev: Akad. Nauk Ukrain. SSR, Inst. Mat., 1986. – P.51–56.  (Russian).

9.

Application of a Gaussian random operator to random elements. (Russian) // Teor. Veroyatnost. i Primenen. V. 31 (1986), No. 4, P. 811–814.

10.

Equations with random maps in Hilbert space. (Russian) // Abstracts from the XXI School-Colloquium on Probability Theory and Mathematical Statistics held in Bakuriani, February 21–March 2, 1987. “Metsniereba”, Tbilisi.

11.

Characterization of strong random Gaussian operators that admit an integral representation with respect to measure with independent values. (Russian) // Theory of random processes, 1987, No. 15, P. 28–34, "Naukova Dumka'', Kiev.

12.

Random maps in Hilbert space. (Russian) // Proceedings of the Conference of Young Scientists held in Kiev, November 24-26, 1986. Kiev: Institute of Mathematics, Academy of Sciences of USSR, 1987.

13.

Smoothness of the solutions of generalized linear stochastic differential equations. (Russian) // Asymptotic problems in the theory of random processes, 1987, Kiev: Acad. Sci. USSR, Inst. Math., P. 67–72.

14.

Equations with random Gaussian operators and a stochastic calculus. (Russian) // Selected problems in the modern theory of random processes, iii, 1988, Kiev: Acad. Sci. USSR, Inst. Math., P. 52–60.

15.

Elements of stochastic differential calculus  (Russian) // Mathematics today '88 (Russian),  105–131, "Vishcha Shkola'', Kiev, 1988.

16.

A representation of strong Gaussian random operators. (Russian) // Theory of random processes, No. 16, 19–23, 108.  Kiev : "Naukova Dumka'',  1988.

17.

On the extension of Clark theorem. (Russian) // Proceedings of the Conference of Young Scientists held in Kiev, June 15-18, 1988. Kiev: Institute of Mathematics, Academy of Sciences of USSR, 1988.

18.

A difference approximation of the Sturm-Liouville problem with white noise in the right-hand side. (Russian) // Kibernetika,  1989,  No. 2, 126–127.

19.

Superposition of random maps in Hilbert space. (Russian) // Teor. Veroyatnost. i Primenen.  34  (1989),  No. 2, 364-370.

20.

Boundary value problems for equations that contain linear stochastic differential operators. (Russian) // Teor. Veroyatnost. i Mat. Statist.  No. 40 (1989), 23–28.

21.

Cavalieri's Principle and its applications. (Ukrainian) // In the world of mathematics. – Kiev: Radianska Shkola, 1989.

22.

Problems of the Republican Tour of the Mathematical Olympiad “Student and the Scientific and Technical Progress”. (Russian) // Mathematics today '89 (Russian), "Vishcha Shkola'', Kiev, 1989  (with N. A. Nazarenko).

23.

Stochastic calculus and stochastic differential equations in infinite dimensional spaces. (Russian) // Abstracts of the V International Vilnius Conference on Probability Theory and Mathematical Statistics held in Vilnius, June 26 – July 1, 1989.

24.

Fourier transform of Wiener functionals and various methods of stochastic integration. (Russian)  // Teor. Veroyatnost. i Primenen.  34  (1989),-  No. 4, 769–773;  translation in Theory Probab. Appl.  34  (1989),  No. 4, 705–709 (1990).

25.

An extended stochastic integral for smooth functionals of white noise. (Russian) // Ukrain. Mat. Zh.  41  (1989),  No. 11, 1460–1466, 1581;  translation in Ukrainian Math. J.  41  (1989),  No. 11, 1252–1258 (1990).

26.

Singular transformations of Wiener functionals and the two-sided Pardoux-Protter integral. (Russian)  // Stochastic analysis and its applications,  37–44, ii, Akad. Nauk Ukrain. SSR, Inst. Mat., Kiev, 1989.

27.

Linear equations that contain an extended stochastic integral. (Russian)

// Ukrain. Mat. Zh.  41  (1989),  No. 12, 1714–1716, 1729;  translation in Ukrainian Math. J.  41  (1989),  No. 12, 1482–1484 (1990).

28.

Stochastic calculus and partial differential equations in infinitely dimensional space // 6-th European young statisticians meeting 21-25 August 1989. Prague. Charles University. –- P. 66–72.

29.

Itô-Volterra equations with an anticipating right-hand side in the absence of moments. (Russian) // Infinite-dimensional stochastic analysis, 41–50, Akad. Nauk Ukrain. SSR, Inst. Mat., Kiev, 1990.

30.

Stochastic integrals with respect to Gaussian random measures. (Russian)  // Teor. Veroyatnost. i Mat. Statist.  No. 44 (1991), 56–63;  translation in Theory Probab. Math. Statist.  No. 44 (1992), 53–59.

31.

Equations with Gaussian random operators, and differential operators of infinite order. (Russian)  // Stochastic equations and boundary theorems  51–61, Akad. Nauk Ukrainy, Inst. Mat., Kiev, 1991.

32.

Local diagonal operators. (Russian) // Fourier series: theory and applications,  27–30, Akad. Nauk Ukrainy, Inst. Mat., Kiev, 1992.

33.

A formula for solving the Itô-Volterra equation with an extended stochastic integral. (Russian) // Random processes and infinite-dimensional analysis,  41–56, Akad. Nauk Ukrainy, Inst. Mat., Kiev, 1992.

34.

Stochastic calculus and linear integral equation //  Probability theory and mathematical statistics (Kiev, 1991),  70–78, World Sci. Publ., River Edge, NJ, 1992.

35.

Random maps and stochastic equations // Trends of 2 Ukrainian- Hungarian conference in Mukachevo, 1992. – Kiev, TViMS. P. 341-349.

36.

On the convergence of iterations disturbed by strong Gaussian random operators //  Stochastics Stochastics Rep.  43  (1993),  No. 1-2, 117–126.

37.

A property of trajectories of extended stochastic integrals (Russian)  // Sibirsk. Mat. Zh.  34  (1993),  No. 5, 38–42, i, vi;  translation in Siberian Math. J.  34  (1993),  No. 5, 825–828.

38.

Smooth Clark representation of Wiener functionals  (Russian) // Theory of stochastic processes, V. 2 (18), (1993) No. 3-4.

39.

Successive approximations of the solution of Cauchy problem under random perturbations (Russian) // Nonlinear boundary value problems of mathematical physics and their applications. Abstracts (1994). Institute of Mathematics, NAS of Ukraine.

40.

Stochastic analysis and a minimization problem   (Russian) //  Ukraïn. Mat. Zh.  46  (1994),  No. 11, 1568–1571;  translation in Ukrainian Math. J.  46  (1994),  No. 11, 1735–1739  (1996).

41.

On stochastic integral representations  (Russian) // Mathematics today '94, No. 9 (Ukrainian),  80–92, "Vishcha Shkola'', Kiev, 1995.

42.

On the family of Itô formulas for the logarithmic processes (Ukrainian)//  Asymptotic analysis of random evolutions,  100–112, Akad. Nauk Ukrainy, Inst. Mat., Kiev, 1994.

43.

On solutions of linear equations with an extended stochastic integral (Russian) // Teor. Veroyatnost. i Primenen.  40  (1995),  No. 3, 508–522;  translation in Theory Probab. Appl.  40  (1995),  No. 3, 456–468 (1996).

44.

On a type of stochastic equation with anticipation (Russian) // Teor. Veroyatnost. i Primenen.  40  (1995),  No. 4, 903--907;  translation in Theory Probab. Appl.  40  (1995),  No. 4, 753–756 (1996).

45.

An approach to the stochastic calculus in the non-Gaussian case // J. Appl. Math. Stochastic Anal.  8  (1995),  No. 4, 361–370.

46.

On the method of characteristics in stochastic analysis  (Russian) // Theory of stochastic processes, V. 1 (17), (1995) No. 1.

47.

Formal stochastic calculus and admissible transformations //  Exploring stochastic laws,  103–109, VSP, Utrecht, 1995.

48.

Local times for measure-valued Ito's stochastic processes // Preprint # 95-142. Case Western Reserve University, Cleveland.- October 12, 1995. – 11 p. (with N.Yu. Goncharuk).

49.

Some characteristics of sequences of iterations with random perturbations (Russian) // Ukraïn. Mat. Zh.  48 (1996),  No. 8, 1047–1063;  translation in Ukrainian Math. J.  48  (1996),  No. 8, 1182–1201 (1997).

50.

Randomly perturbed dynamic systems and sojourn measures // Abstracts of the international conference "Asymptotic methods in theory of nonlinear oscillations", Kiev, August,18-23, 1997. – P. 53.

51.

Smooth Stationary Solutions of Quasilinear Stochastic Partial Differential Equations: 1. Finite Mass // Preprint #97–145 Department of Mathematics Case Western Reserve University Cleveland, Ohio. 19 p. (with Peter Kotelenez).

52.

Anticipating equations and filtration problem // Theory of stochastic processes, 1997. V.3(19), issue 1–2.   P. 154-163.

53.

Stochastic integration and a class of Gaussian random processes (Russian) //  Ukraïn. Mat. Zh.  50  (1998),  No. 4, 485–-495;  translation in Ukrainian Math. J.  50  (1998),  No. 4, 550–561 (1999).

54.

Conditional measures for diffusion processes and anticipating stochastic equations // Proceedings of the Donetsk Colloquium on Probability Theory and Mathematical Statistics (1998). Theory Stoch. Process.  4  (1998),  No. 1-2, 17–24.

55.

Visitation measures and an ergodic theorem for a sequence of iterations with random perturbations (Russian) //  Ukraïn. Mat. Zh.  51  (1999),  No. 1, 123--127;  translation in Ukrainian Math. J.  51  (1999),  No. 1, 134–139.

56.

Stochastic integrals with respect to compatible random measures (Russian) // Ukraïn. Mat. Zh.  52  (2000),  No. 8, 1062–1074;  translation in Ukrainian Math. J.  52  (2000),  No. 8, 1215–1229 (2001).

57.

Measurable functionals and finitely absolutely continuous measures on Banach spaces  (Russian) //  Ukraïn. Mat. Zh.  52  (2000),  No. 9, 1194–1204;  translation in Ukrainian Math. J.  52  (2000),  No. 9, 1366–1379 (2001).

58.

A variant of the Skorokhod theorem for Markov sequences // In the volume “Skorohod ideas in probability theory”. Edited by V.Korolyuk, N.Portenko, H.Syta. Institute of mathematics Ukrainian Academy of Sciences. P. 147-151.

59.

Sojourn measures for switching processe // Proceedings of the Third Ukrainian-Scandinavian Conference in Probability Theory and Mathematical Statistics (Kiev, 1999). Theory Stoch. Process.  5  (1999),  No. 3-4, 57–63. (with N. A. Denis’evskii).

60.

Properties of the random measures // Theory Stoch. Process.  6  (2000),  No. 1-2, 26–33.

61.

Measure-valued Markov processes and stochastic flows (Russian) //  Ukraïn. Mat. Zh.  54  (2002),  No. 2, 178--189;  translation in Ukrainian Math. J.  54  (2002),  No. 2, 218–232.

62.

Stochastic flows with interaction, and measure-valued Markov processes (Russian)// Dokl. Akad. Nauk  388  (2003),  No. 2, 151–154.

63.

Random mappings and generalized additive functionals of the Wiener process (Russian) // Teor. Veroyatnost. i Primenen.  48  (2003),  No. 1, 43–61;  translation in Theory Probab. Appl.  48  (2003),  No. 1, 63–79 (with V. V. Bakun).

64.

Long-time behaviour of measure-valued processes correspondent to stochastic flows with interactions // Theory Stoch. Process.  9  (2003),  No. 1-2, 52–59 (with M. P. Karlikova).

65.

Stochastic differential equations and random measures in function spaces (Russian) // Dokl. Akad. Nauk  399  (2004),  No. 3, 303–306.

66.

Measure-valued Markov processes and stochastic flows on abstract spaces // Stoch. Stoch. Rep.  76  (2004),  No. 5, 395–407.

67.

One version of the Clark representation theorem for Arratia flows // Theory Stoch. Process.  11  (2005),  No. 3-4, 63–70.

68.

Smoothing problem in anticipating scenario //  Ukraïn. Mat. Zh.  57  (2005),  No. 9, 1218–1234;  translation in Ukrainian Math. J.  57  (2005),  No. 9, 1424–1441.

69.

Some remarks on a Wiener flow with coalescence  (Russian) // Ukraïn. Mat. Zh.  57  (2005),  No. 10, 1327–1333;  translation in Ukrainian Math. J.  57  (2005),  No. 10, 1550–1558.

70.

On the localization of an extended stochastic integral  (Russian) //  Mat. Sb.  197  (2006),  No. 9, 19–42;  translation in Sb. Math.  197  (2006),  No. 9-10, 1273–1295 (with A. M. Gomilko).

71.

A stochastic integral with respect to the Arratia flow  (Russian) // Dokl. Akad. Nauk  410  (2006),  No. 2, 156–157.

72.

Matematika s’ogodnī '07  (Ukrainian) [Mathematics today '07] //  Edited by A. A. Dorogovtsev. Matematika s’ogodnī [Mathematics Today], 13. “Fakt”, Kiev, 2007. 244 pp.

73.

On the area of a Wiener sausage and stochastic analysis (Russian) // Mathematics today '07 (Ukrainian),  25–46, Mat. S’godnī, 13, "Fakt'', Kiev, 2007.

74.

Conditioning of Gaussian functionals and orthogonal expansion // Theory Stoch. Process.  13  (2007),  No. 3, 29–37.

75.

Systems of Brownian particles with coalescing // Proceedings of the Institute of Mathematics, NAS of Ukraine, V 4 (2007), No. 3.

76.

Matematika s’ogodnī '08  (Russian) [Mathematics today '08] // Edited by A. A. Dorogovtsev. Matematika s’ogodnī [Mathematics Today], 14. “Fakt”, Kiev, 2008. 179 pp. ISBN: 978-966-359-315-9.

77.

Boundary value problems for stochastic equations with anticipation (Russian) // Dokl. Akad. Nauk  418  (2008),  No. 4, 443–446;  translation in Dokl. Math.  77  (2008),  No. 1, 76–79.

78.

Matematika s’ogodnī '09 (Russian) [Mathematics today '09] // Edited by A. A. Dorogovtsev. Matematika s’ogodnī [Mathematics Today], 15. “Osvita Ukrainy”, 2009. 122 p.

79.

Large deviations for stochastic flows with interaction (Ukrainian) // Dokl. Akad. Nauk    (2009),  No. 1 (with O. V. Ostapenko).

80.

Entropy of stochastic flows  (Russian) //  Mat. Sb.  201  (2010),  No. 5, 17--26;  translation in Sb. Math.  201  (2010),  No. 5–6, 645–653.

81.

Large deviations for flows of interacting Brownian motions //  Stoch. Dyn.  10  (2010),  No. 3, 315–339 (with O. V. Ostapenko).

82.

Semigroups of finite-dimensional random projections // Lithuanian Mathematical Journal, V. 51 (2011), No. 3.

83.

On regularization of the formal Fourier-Wiener transform of the self-intersection local time of planar Gaussian process // Theory of Stoch. Processes, V. 17 (33) (2011), No. 1 (with O. L. Izyumtseva).

84.

Krylov-Veretennikov expansion for coalescing stochastic flows // Comm. on Stoch. Analysis, V. 6 (2012), No. 3, pp. 421-435.

85.

Iterated logarithm law for sizes of clusters in Arratia flow // Theory Stoch. Process., V. 18 (2012), No. 2, pp. 1-7 (with A. V. Gnedin and M. B. Vovchanskii).

86.

Asymptotic and geometric properties of compactly perturbed Wiener process and self-intersection local time // Comm. on Stoch. Analysis, V. 7 (2013), No. 2, pp. 337-348 (with O. L. Izyumtseva).

87.

Local self-intersection times for Gaussian processes in the plane // Dokl. Akad. Nauk, V. 454 (2014), No. 3, pp. 262-264 (with O. L. Izyumtseva).

88.

Geometric entropy in Banach spaces // Theory Stoch. Process., V. 19 (2014), No. 2, pp. 10-30 (with Mikhail Popov).

89.

Anatolii Skorokhod (10 September 1930–3 January 2011).// Eur. Math. Soc. Newsl. No.94 (2014), 24–31 (with Buldygin, Valerii; Portenko, Mykola; Kadyrova, Irina).

90.

An analysis of stochastic flows //Commun. Stoch. Anal. 8 (2014), no. 3, 331–342 (with Nishchenko, I. I.)

91.

Properties of Gaussian local times // Lith. Math. J. 55 (2015), no. 4, 489–505 (with Izyumtseva, Olga).

92.

On self-intersection local times for generalized Brownian bridges and the distance between step functions // Theory Stoch. Process. 20(2015), no. 1, 1–13 (with Izyumtseva, O. L.).

93.

Self-intersection local times // Ukraïn. Mat. Zh. 68 (2016), no. 3, 290--340; translation in Ukrainian Math. J. 68 (2016), no. 3, 325–379  (with Izyumtseva, O. L. ) (Russian)

94.

Transformations of Wiener measure and orthogonal expansions // Infin. Dimens. Anal. Quantum Probab. Relat. Top. 19 (2016), no. 3,1650018, 18 pp.(with Riabov, Georgii )

95.

Clark formula for local time for one class of Gaussian processes // Commun. Stoch. Anal. 10 (2016), no. 2,195–217 (with Izyumtseva, O. L.; Riabov, G. V.; Salhi, Naoufel )

 

 

 

 

 

 

 

 

 

 

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