Jerzy Zabczyk, Professor
Institute of Mathematics, Polish Academy of Sciences

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PAPERS:

1. B. Goldys, S. Peszat, J. Zabczyk, GAUSS-MARKOV PROCESSES ON HILBERT SPACES, Transactions of the American Mathematical Society, to appear
2. S. Peszat, J. Zabczyk, TIME REGULARITY FOR STOCHASTIC VOLTERRA EQUATIONS BY THE DILATION THEOREM, Journal of Mathematical Analysis and Applications 409 (2014), 676-683.
3. L. Pandolfi, E. Priola, J. Zabczyk, LINEAR OPERATOR INEQUALITY AND NULL CONTROLLABILITY WITH VANISHING ENERGY FOR BOUNDARY CONTROL SYSTEMS, SIAM J. Control and Optimization 51 (2013), 629-659.
4. S. Peszat, J. Zabczyk, TIME REGULARITY OF SOLUTIONS TO LINEAR EQUATIONS WITH LÉVY NOISE IN INFINITE DIMENSIONS, Stochastic Processes and their Applications 123 (2013), 719-751.
5. M. Barski, J.Zabczyk, HEATH-JARROW-MORTON-MUSIELA EQUATION WITH LÉVY PERTURBATION, Journal of Differential Equations 253 (2012), 2657-2697.
6. A. Swiech, J. Zabczyk, UNIQUENESS FOR INTEGRO-PDE IN HILBERT SPACE, Potential Analysis 38 (2013), 233-259.
7. E. Priola, A. Shirikyan, L. Xu, J. Zabczyk, EXPONENTIAL ERGODICITY AND REGULARITY FOR EQUATIONS WITH LÉVY NOISE, Stochastic Processes and Applications 122 (2012), 106-133.
8. E. Priola, L. Xu, J. Zabczyk, EXPONENTIAL MIXING FOR SOME SPDEs WITH LÉVY NOISE, Stochastic and Dynamics 11 (2011), 521-534.
9. M. Barski, J. Zabczyk, FORWARD RATE MODELS WITH LINEAR VOLATILITIES, Finance and Stochastics 16 (2012), 537-560.
10. T. Schmidt, J. Zabczyk, CDO TERM STRUCTURE MODELLING WITH LÉVY PROCESSES AND THE RELATION TO MARKET MODELS, Int. J. Theor. Appl. Finance, 15 (2012), No. 1.
11. A. Swiech, J. Zabczyk, LARGE DEVIATIONS FOR STOCHASTIC PDE WITH LÉVY NOISE, J. Funct. Anal. 260 (2011), 674-723.
12. M. Baran, J. Zabczyk, COMPLETENESS OF BOND MARKET WITH INFINITE NUMBER OF RANDOM FACTORS, Int. J. Theor. Appl. Finance 13 (2010), 635-656.
13. Z. Brzezniak, B. Goldys, P. Imkeller, S. Peszat, E. Priola, J. Zabczyk, TIME IRREGULARITY OF GENERALIZED ORNSTEIN-UHLENBECK PROCESSES, C. R. Acad. Sci. Paris Sér. Math. 348 (2010), 273-276.
14. M. Barski, J. Jakubowski, J. Zabczyk, ON INCOMPLETENESS OF BOND MARKET WITH INFINITE NUMBER OF RANDOM FACTORS, Mathematical Finance 21 (2011), 541-556.
15. Z. Brzezniak, J. Zabczyk, REGULARITY OF ORNSTEIN-UHLENBECK PROCESSES DRIVEN BY A LÉVY WHITE NOISE, Potential Analysis 32 (2010), 153-188.
16. E. Priola, J. Zabczyk, STRUCTURAL PROPERTIES OF SEMILINEAR SPDES DRIVEN BY CYLINDRICAL STABLE PROCESSES, Probab. Theory Relat. Fields 149 (2011), 97-137.
17. E. Priola, J. Zabczyk , DENSITIES FOR ORNSTEIN-UHLENBECK PROCESSES WITH JUMPS, Bull. London Math. Soc. 41 (2009), 41-50.
18. E. Priola, J. Zabczyk, ON LINEAR EVOLUTION EQUATIONS FOR A CLASS OF CYLINDRICAL LÉVY NOISE, Proceedings of Levico Conference on Stochastic Partial Differential Equations and Applications, Editors: G. Da Prato and L. Tubaro, Quaderni di Matematica, Dipartimento di Matematica, Seconda Università di Napoli, 25 (2010), 223-242.
19. J. Jakubowski, J. Zabczyk , EXPONENTIAL MOMENTS FOR HJM MODELS WITH JUMPS, Finance and Stochastics 11 (2007), 429-449.
20. G. Tessitore, J. Zabczyk, WONG-ZAKAI APPROXIMATIONS OF STOCHASTIC EVOLUTION EQUATIONS, Journal of Evolution Equations 6 (2006), 621-655.
21. E. Priola, J. Zabczyk, ON BOUNDED SOLUTIONS TO CONVOLUTION EQUATIONS, Proc. Amer. Math. Soc. 134 (2006), 3275-3286 (electronic).
22. K. Twardowska, J. Zabczyk, QUALITATIVE PROPERTIES OF SOLUTIONS TO STOCHASTIC BURGERS' SYSTEM OF EQUATIONS, Stochastic Partial Differential Equations and Applications VII, Lect. Notes Pure Appl. Math. 245 (2006), 311-322.
23. E. Priola, J. Zabczyk, HARMONIC FUNCTIONS FOR GENERALIZED MEHLER SEMIGROUPS, Stochastic Partial Differential Equations and Applications VII, Lect. Notes Pure Appl. Math. 245 (2006), 243-256.
24. S. Peszat, J. Zabczyk, STOCHASTIC HEAT AND WAVE EQUATIONS DRIVEN BY AN IMPULSIVE NOISE, Stochastic Partial Differential Equations and Applications VII, Lect. Notes Pure Appl. Math. 245 (2006), 229--242.
25. J. Palczewski, J. Zabczyk, PORTFOLIO DIVERSIFICATION WITH MARKOVIAN PRICES, Probab. Math. Statist. 25 (2005), Acta Univ. Wratislav. No. 2784, 75--95.
26. K. Twardowska, J. Zabczyk, A NOTE ON STOCHASTIC BURGERS’ SYSTEM OF EQUATIONS, Stochastic Analysis and Applications 22 (2004), 1641-1670.
27. E. Priola, J. Zabczyk, LIOUVILLE THEOREMS FOR NON-LOCAL OPERATORS, Journal on Functional Analysis 216 (2004), 455-490.
28. E. Priola, J. Zabczyk, NULL CONTROLLABILITY WITH VANISHING ENERGY, SIAM Journal on Control and Optimization 42 (2003), 1013-1032.
29. D. Filipovic, J. Zabczyk, MARKOVIAN TERM STRUCTURE MODELS IN DISCRETE TIME, Annals of Applied Probability 12 (2002), 710-729.
30. G. Tessitore, J. Zabczyk, PRICING OPTIONS FOR MARKOVIAN MODELS, Proceedings of a Conference on Stochastic Processes, Eds. R. Buckdahn, H-J. Engelbert and M. Yor, Taylor and Francis, 2002, 249-268.
31. Z. Brzezniak, S. Peszat, J. Zabczyk, CONTINUITY OF STOCHASTIC CONVOLUTIONS, Czech. Math. J. 51 (2001), 679-684.
32. G. Da Prato, M. Fuhrman, J. Zabczyk, A NOTE ON REGULARIZING PROPERTIES OF ORNSTEIN-UHLENBECK PROCESSES IN INFINITE DIMENSIONS, Stochastic Partial Differential Equations, Eds. G. Da Prato and L. Tubaro, Marcel Dekker, 2002, 167-182.
33. J. Zabczyk, A MINI COURSE ON STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS, Progress in Probability, Birkhäuser 49 (2001), 257-284.
34. G. Tessitore, J. Zabczyk, TROTTERS FORMULA FOR TRANSITION SEMIGROUPS, Semigroup Forum 63 (2001), 114-126.
35. A. Karczewska, J. Zabczyk, REGULARITY OF SOLUTIONS OF STOCHASTIC VOLTERRA EQUATIONS, Rend. Mat. Acc. Lincei ser. 9 11 (2000), 141-154.
36. J. Zabczyk, STOCHASTIC INVARIANCE AND CONSISTENCY OF FINANCIAL MODELS, Rend. Mat. Acc. Lincei ser. 9 11 (2000), 67-80.
37. J. Zabczyk, BELLMAN’S INCLUSIONS AND EXCESSIVE MEASURES, Probability and Mathematical Statistics 201 (2001), 101-122.
38. S. Peszat, J. Zabczyk, NONLINEAR STOCHASTIC WAVE AND HEAT EQUATIONS, PTRF 116 (2000), 421-443.
39. A. Karczewska, J. Zabczyk, STOCHASTIC PDEs WITH FUNCTION-VALUED SOLUTIONS, Proceedings of the Colloquium ”Infinite-Dimensional Stochastic Analysis” of the Royal Netherlands Academy of Arts and Sciences, Amsterdam 1999, Eds. Ph. Clement, F. den Hollander, J. van Neerven and B. de Pagter, North Holland, 197-216.
40. J. Zabczyk, PARABOLIC EQUATIONS ON HILBERT SPACES, LNiM 1715 (1999), 117-213.
41. G. Tessitore, J. Zabczyk, INVARIANT MEASURES FOR STOCHASTIC HEAT EQUATIONS, Probability and Mathematical Statistics 18 (1998), 271-287.
42. G. Tessitore, J. Zabczyk, STRICT POSITIVITY FOR STOCHASTIC HEAT EQUATIONS, Stochastic Processes and Applications 77 (1998), 83-98.
43. G. Da Prato, J. Zabczyk, DIFFERENTIABILITY OF THE FEYNMAN-KAC SEMIGROUP AND A CONTROL APPLICATION, Rendiconti Lincei: Scienze Fisiche e Naturali, Serie IX 8 (1997), 183-188.
44. J. Zabczyk, INFINITE DIMENSIONAL DIFFUSIONS IN MODELLING AND ANALYSIS, Jahresberichte der DMV 101 (1999), 47-59.
45. J. M. A. M. Neerven, J. Zabczyk, NORM DISCONTINUITY OF ORNSTEIN-UHLENBECK SEMIGROUPS, Semigroup Forum 59 (1999), 384-403.
46. J. Zabczyk, STOPPING PROBLEMS ON POLISH SPACES, Annales Univ. M. Curie-Sklodowska Sect. A 51 (1997), 181-199.
47. G. Da Prato, B. Goldys, J. Zabczyk, ORNSTEIN-UHLENBECK SEMIGROUPS IN OPEN SETS OF HILBERT SPACES, C. R. Acad. Sci. Paris Serie I 325 (1997), 433-438.
48. S. Peszat, J. Zabczyk, STOCHASTIC EVOLUTION EQUATIONS WITH A SPATIALLY HOMOGENOUS WIENER PROCESS, Stochastic Processes and Applications 72 (1997), 187-204.
49. N. U. Ahmed, J. Zabczyk, PARTIALLY OBSERVED OPTIMAL CONTROLS FOR NONLINEAR INFINITE DIMENSIONAL STOCHASTIC SYSTEMS, Dynamic Systems and Applications 5 (1996), 521-538.
50. N. U. Ahmed, M. Fuhrman, J. Zabczyk, ON FILTERING EQUATIONS IN INFINITE DIMENSIONS, J. Funct. Anal. 143 (1997), 180-204.
51. M. Tessitore, J. Zabczyk, PRICING OPTIONS FOR MULTINOMIAL MODELS, Bull. Pol. Acad. Sci. 44 (1996), 363-380.
52. J. Zabczyk, PRICING OPTIONS BY DYNAMIC PROGRAMMING, Stochastic Processes and Related Topics, Eds. H. J. Engelbert, H. Follmer and J. Zabczyk, Gordon and Breach, 1996, 153-160.
53. G. Da Prato, J. Zabczyk, CONVERGENCE TO EQUILIBRIUM FOR CLASSICAL AND QUANTUM SPIN SYSTEMS, Probability Theory and Related Fields 103 (1995), 529-552.
54. S. Peszat, J. Zabczyk, STRONG FELLER PROPERTY AND IRREDUCIBILITY FOR DIFFUSIONS ON HILBERT SPACES, Annals of Probability 23 (1995), 157-172.
55. G. Da Prato, J. Zabczyk, REGULAR DENSITIES OF INVARIANT MEASURES FOR NONLINEAR STOCHASTIC EQUATIONS, J. Funct. Anal. 130 (1995), 427-449.
56. G. Da Prato, D. Elworthy, J. Zabczyk, STRONG FELLER PROPERTY FOR STOCHASTIC SEMILINEAR EQUATIONS, Stoch. Anal. and Applications 13 (1995), 35-45.
57. G. Da Prato, J. Zabczyk, EVOLUTION EQUATIONS WITH WHITE-NOISE BOUNDARY CONDITIONS, Stochastics and Stochastics Reports 42 (1993), 167-182.
58. G. Da Prato, J. Zabczyk, ON INVARIANT MEASURES FOR SEMILINEAR STOCHASTIC EQUATIONS WITH DISSIPATIVE NONLINEARITIES, Proc. Conf. Stoch. Part. Differ. Equations and Appl., Eds. B. L. Rozowski and R. B. Sowers, LNiCIS 176 (1992), 38-42.
59. J. Zabczyk, THE FRACTIONAL CALCULUS AND STOCHASTIC EVOLUTION EQUATIONS, Barcelona Seminar on Stochastic Analysis, Eds. D. Nualart and M. Sanz-Sole, Birkhäuser, 1993, 222-234.
60. G. Da Prato, D. Gatarek, J. Zabczyk, INVARIANT MEASURES FOR SEMILINEAR STOCHASTIC EQUATIONS, Stoch. Anal. Appl. 10 (1992), 387-408.
61. G. Da Prato, J. Zabczyk, A NOTE ON STOCHASTIC CONVOLUTION, Stoch. Anal. Appl. 10 (1992), 143-153.
62. J. Zabczyk, LAW EQUIVALENCE OF ORNSTEIN-UHLENBECK PROCESSES, Proc. The Third Nagoya Conf. Gaussian Random Fields, Eds. K. Ito and T. Hida, World Scientific 1992, 420-432.
63. G. Da Prato, J. Zabczyk, NON-EXPLOSION, BOUNDEDNESS AND ERGODICITY FOR STOCHASTIC SEMILINEAR EQUATIONS, J. Diff. Equations 98, 181-195.
64. G. Da Prato, A. Pritchard, J. Zabczyk, ON MINIMUM ENERGY PROBLEMS, SIAM J. Control and Optimization 29 (1991), 209-221.
65. G. Da Prato, J. Zabczyk, SMOOTHING PROPERTIES OF THE KOLMOGOROFF SEMIGROUPS IN HILBERT SPACES, Stochastics and Stochastics Reports 35 (1991), 63-77.
66. J. Zabczyk, ON LARGE DEVIATIONS FOR STOCHASTIC EVOLUTION EQUATIONS, Proceedings of the 6th IFIP working Conference on Stochastic System and Optimization, Warsaw, 1988, Lecture Notes in Computing and Information Sciences 136.
67. A. Sierocinski, J. Zabczyk, ON A PACKING PROBLEM, Bull. Pol. Acad. Sci. 11/12 (1989), 104-118.
68. J. Zabczyk, SYMMETRIC SOLUTION OF SEMILINEAR STOCHASTIC EQUATIONS, Proceedings of a Conference on Stochastic Partial Differential Equations, Trento, Italy, 1987, Lecture Notes in Mathematics 1390 (1989), 237-256.
69. R. Rempala, J. Zabczyk, ON THE MAXIMUM PRINCIPLE FOR DETERMINISTIC IMPULSE CONTROL PROBLEMS, J. Optimization Theory and Applications 59 (1988), 281-288.
70. G. Mazziotto, L. Stettner, J. Szpirglas, J. Zabczyk, ON IMPULSE CONTROL WITH PARTIAL OBSERVATION, SIAM J. on Control and Optimization 26 (1988), 964-984.
71. J. Zabczyk, SOME COMMENTS ON STABILIZABILITY, Journal of Applied Mathematics and Optimization 19 (1988), 1-9.
72. G. Da Prato, J. Zabczyk, A NOTE ON SEMILINEAR STOCHASTIC EQUATIONS, Journal of Differential and Integral Equations 1 (1988), 143-155.
73. W. Smolenski, R. Sztencel, J. Zabczyk, LARGE DEVIATIONS ESTIMATES FOR SEMILINEAR STOCHASTIC EQUATIONS, Proceedings of the IFIP Conference on Stochastic Differential Systems, Eisenach, Lecture Notes in Control and Information Sciences 96 (1987), 218-231.
74. G. Da Prato, S. Kwapien, J. Zabczyk, REGULARITY OF SOLUTIONS OF LINEAR STOCHASTIC EQUATIONS IN HILBERT SPACES, Stochastics 23 (1987), 1-23.
75. J. Zabczyk, STABLE DYNAMICAL SYSTEMS UNDER SMALL PERTURBATIONS, Journal of Mathematical Analysis and Applications 125 (1987), 568-588.
76. J. Zabczyk, EXIT PROBLEM FOR INFINITE DIMENSIONAL SYSTEMS, Proceedings of a Workshop on Stochastics PDE’s and Applications, Trento 1985, Lecture Notes in Mathematics 1236 (1987), 239-257.
77. J. Zabczyk, EXIT PROBLEM AND CONTROL THEORY, Systems and Control Letters 6 (1985), 162-172.
78. J. Zabczyk, STOPPING PROBLEMS IN STOCHASTIC CONTROL, Proceedings of the International Congress of Mathematicians, Warsaw, 1984, 1425-1437.
79. J. Zabczyk, STRUCTURAL PROPERTIES AND LIMIT BEHAVIOUR OF LINEAR STOCHASTIC SYSTEMS IN HILBERT SPACES, Banach Center Publications 14 (1985), 593-611.
80. J. Zabczyk, CONTROLLABILITY OF STOCHASTIC SYSTEMS, Proceedings of the 2nd Bad Honnef Conference on Stochastic Differential Systems, Lecture Notes in Control and Information Sciences 43 (1982), 144-154.
81. J. Zabczyk, STATIONARY DISTRIBUTIONS FOR LINEAR EQUATIONS DRIVEN BY GENERAL NOISE, Bull. Pol. Acad. Sci. 31 (1983), 197-209.
82. J. Zabczyk, STOPPING GAMES FOR SYMMETRIC MARKOV PROCESSES, Probability and Mathematical Statistics 4 (1984), 185-196.
83. A. Pritchard, J. Zabczyk, STABILITY AND STABILIZABILITY OF INFINITE DIMENSIONAL SYSTEMS, SIAM Review 23 (1981), 25-52.
84. J. Zabczyk, CONTROLLABILITY OF STOCHASTIC LINEAR SYSTEMS, System and Control Letters 1 (1981), 25-31.
85. L. Stettner, J. Zabczyk, STRONG ENVELOPES OF STOCHASTIC PROCESSES AND A PENALTY METHOD, Stochastics 4 (1981), 267-282.
86. J. Zabczyk, STABILIZATION OF BOUNDARY CONTROL SYSTEMS, Proceedings of International Symposium on System Optimization, Lecture Notes in Control and Information Sciences 14 (1979), 321-332.
87. J. Zabczyk, ON THE STABILITY OF INFINITE DIMENSIONAL LINEAR STOCHASTIC SYSTEMS, Banach Center Publications 5 (1979), 273-281.
88. J. Zabczyk, INTRODUCTION TO THE THEORY OF OPTIMAL STOPPING, Proceedings of the 1st Bad Honnet Conference on Stochastic Systems, 1979, Lecture Notes in Control and Information Sciences 16 (1979), 227-250.
89. Z. Ciesielski, J. Zabczyk, A NOTE ON A SELECTION PROBLEM, Banach Center Publications 5 (1979), 47-51.
90. J. Zabczyk, ON DECOMPOSITION OF GENERATORS, SIAM J. Control 16 (1978), 523-534. Erratum: On decomposition of generators, SIAM J. Control and Optimization 18 (1980), 325.
91. R. Cowan, J. Zabczyk, AN OPTIMAL SELECTION PROBLEM ASSOCIATED WITH THE POISSON PROCESS, Theory of Probability and Appl. 23 (1978), 606-614.
92. J. Zabczyk, STABILITY PROPERTIES OF THE DISCRETE RICCATI OPERATOR EQUATION, Kybernetika 13 (1977), 1-10.
93. J. Zabczyk, COMPLETE STABILIZABILITY IMPLIES EXACT CONTROLLABILITY, Seminarul Ecuati Functionale N. 38, Timisoara 1976, Romania, 1-7.
94. J. Zabczyk, A NOTE ON C(O)-SEMIGROUPS, Bull. Pol. Acad. Sci. 23 (1975), 895-898.
95. J. Zabczyk, REMARKS ON THE ALGEBRAIC RICCATI EQUATION IN HILBERT SPACE, J. Appl. Math. and Optimization 2 (1976), 251-258.
96. J. Zabczyk, A NOTE ON SEMIPOLAR SETS FOR PROCESSES WITH INDEPENDENT INCREMENTS, Proceedings of Winter School on Probability, Karpacz 1975. Lecture Notes in Mathematics 472 (1975), 277-283.
97. J. Zabczyk, A NOTE ON THE EXPONENTIAL STABILITY OF A MATRIX RICCATI EQUATION OF STOCHASTIC CONTROL, Kybernetika 11 (1975), 218-222.
98. J. Zabczyk, ON OPTIMAL STOCHASTICS CONTROL OF DISCRETE-TIME PARAMETER SYSTEMS IN HILBERT SPACES, SIAM J. Control 13 (1975), 1217-1234.
99. J. Zabczyk, REMARKS ON THE CONTROL OF DISCRETE-TIME DISTRIBUTED PARAMETER SYSTEMS, SIAM J. Control 12 (1974), 161-176.
100. T. Bojdecki, J. Los, T. Skomorochin, J. Zabczyk, SOME PROPERTIES OF ORDERED FINITE DIMENSIONAL SPACES. Proceedings of the Conference on Mathematical Methods of Economy, Warsaw 1974, 314-327.
101. J. Zabczyk, OPTIMAL CONTROL BY MEANS OF SWITCHINGS, Studia Math. 45 (1973), 161-170.
102. J. Zabczyk, REMARKS ON STOCHASTIC DERIVATION, Bull. Pol. Acad. Sci. 21 (1973), 263-269.
103. J. Zabczyk, ON SOME INTEGRAL EQUATION, Colloquium Math. 25 (1972), 315-318.
104. J. Zabczyk, A MATHEMATICAL CORRECTION PROBLEM, Kybernetika 8 (1972), 317-324.
105. J. Zabczyk, SUR LA THEORIE SEMI-CLASSIQUE DU POTENTIEL POUR LES PROCESSUS A ACCROISSEMENTS INDEPENDENT, Studia Math. 35 (1970), 227-247.
106. J. Zabczyk, PROBABILITIES D’ATTEINTES D’UN ENSEMBLE DANS LES CHAINES DE MARKOV, Bull. Pol. Acad. Sci. 7 (1969), 827-831.