Prof. Marek Capi?ski

PAPERS - Mathematics
40.  Derivative pricing methodology in continuous-time models , (with P.E.Kopp), Applied Mathematics Letters,  Volume 25, (2012) 2137-2139
39.  Model of credit risk based on cash flow , Computers and Mathematics with Applications, Volume 54, (2007) 449-506
38.  Stochastic flow and attractors for stochastic Navier-Stokes equations (with N. Cutland), Probability Theory and Related Fields, Volume 115, Issue 1,(1999) 121-151
37. Measure attractors for stochastic Navier-Stokes equations (with N. Cutland), Electronic Journal of Probability 3, Paper 8 (1998), 1-15; http://math.washington.edu/~ejpecp
36. Stochastic Euler equations (with N. Cutland), Annals of Applied Probability, vol. 9 no 3 (1999)
35. On the existence of solutions of stochastic Navier-Stokes equations (with S.Peszat), Nonlinear Analysis, Theory Methods and Applications, 44 (2001), 141-177
34. Attractors for 3-D Navier-Stokes equations (with N. Cutland), Proceedings of the Royal Society London A, 453 (1997), 2413-2426
33. Local existence and uniqueness to 3-D stochastic Navier-Stokes equations (with S.Peszat), Nonlinear Differential Equations and Applications 4 (1997), 185-200.
32. Continuity of measures on Hilbert spaces (with J.Parker), Universitatis Iagellonicae Acta Mathematica 33 (1996), 33-47.
31. Nonstandard approach to hydrodynamics, Proceedings of NATO Advanced Studies Institute, Edinburgh 1996, Series C, vol.493.pp. 341-356.
30. Foias and Hopf statistical solutions for stochastic Navier-Stokes equations, (with N.Cutland), Stochastics and Stochastics Reports 52 (1995), 193-205.
29. Stochastic equations in Hilbert space with application to Navier-Stokes equations in any dimension, (with D.Gatarek), Journal of Functional Analysis 126 (1994), 26-35.
28. Statistical solutions of stochastic Navier-Stokes equations. (with N.Cutland), Indiana University Mathematics Journal 43:3 (1994), 927-940.
27. Navier-Stokes equations (with N.Cutland), in: Advances in Analysis, Probability, and Mathematical Physics -- Contributions from Nonstandard Analysis, S.Albeverio, W.A.J.Luxemburg, M.P.H.Wolff (eds.),Kluwer, Dordrecht 1994.
26. Nonstandard approach to the uniqueness problem for the Navier-Stokes equations, (with N.Cutland), Monatshefte fur Mathematik 117(1994), 51-61.
25. Nonstandard methods for Navier-Stokes equations, (with N.Cutland), Revista Colombiana de Matematicas, Vol. XXVII (1993), 25-34.
24. A note on uniqueness for stochastic Navier-Stokes equations, Univ. Iagell. Acta Math. 30(1993), 219-228.
23. Navier-Stokes equations with mutliplicative noise (with N.Cutland), Nonlinearity 6 (1993), 71-77.
22. The Euler equation: a uniform nonstandard construction of a global flow, invariant measures, and statistical solutions (with N.Cutland), Annals of Applied Probability 3:1(1993), 212-227.
21. Deterministic attractors of ergodic stochastic flows (with Z.Brzezniak and F.Flandoli), Probability Theory and Related Fields 95(1993), 87-102.
20. Stochastic Navier-Stokes equations with multiplicative noise, (with Z.Brzezniak and F.Flandoli), Stochastic Analysis and Applications 10:5 (1992), 523-532.
19. A simple example of intrinsic turbulence (with N.Cutland), Journal of Differential Equations, 98:1 (1992), 19-33.
18. A simple nonstandard proof of existence of weak and statistical solutions of Navier-Stokes equations, (with N.Cutland), Proceedings of the Royal Society London, Ser. A 436 (1992), 1-11.
17. Statistical solutions of the Navier-Stokes equations by nonstandard densities (with N.Cutland), Mathematical Models and Methods in Applied Sciences 1:4 (1991) 447-460.
16. Stochastic Navier-Stokes equations (with N.Cutland), Acta Applicandae Mathematicae 25 (1991) 59-95.
15. Stochastic partial differential equations and turbulence (with Z.Brzezniak and F.Flandoli), Mathematical Models and Methods in Applied Sciences 1:1 (1991), 41-59.
14. Statistical solutions of PDEs by nonstandard densities (with N.Cutland), Monatshefte fur Mathematik 111 (1991), 99-117.
13. Hopf equation for certain non-linear differential delay equation and invariant measures for corresponding dynamical systems, Universitatis Iagiellonicae Acta Mathematica 28 (1990), 171-175
12. Hopf equation for diffusion in random velocity field (with B.Szafirski), Bull. Acad. Pol. Sci. Math. 38:1-12 (1990), 93-97.
11. Approximation of white noise in stochastic partial differential equations (with Z.Brzezniak and F.Flandoli), in: Stochastic Processes, Physics, and Geometry, (Ascona/Locarno, July 1988), World Scientific, pp.256-268.
10. Approximation for diffusion in random fields (with Z.Brzezniak and F.Flandoli), Stochastic Analysis and Applications 8:3 (1990), 293-313.
9. A convergence result for stochastic partial differential equations (with Z.Brzezniak and F.Flandoli), Stochastics 24:4 (1988), 423-445.
8. On the solutions of the Hopf equation for heat transfer (with B.Szafirski), Bull. Acad. Pol. Sci. 30 (1982), 229-233.
7. On turbulent statistical solutions of the heat equation, Zeszyty Naukowe Uniwersytetu Jagiellonskiego, Prace Matematyczne, Zeszyt 23 (1982), 111-115.
6. Statistical investigation of the heat equation (with B.Szafirski), Bull. Acad. Pol. Sci. Ser. Math. 29 (1981), 553-560.
5. Statistical solutions of the heat equation, Zeszyty Naukowe Uniwersytetu Jagiellonskiego, Prace Matematyczne, Zeszyt 22 (1981), 111-118.
4. Statistical solutions of differential equations in turbulent heat transfer (with B.Szafirski), Bull. Acad. Pol. Sci. Ser. Math. 28 (1980), 117-123.
3. Equivalence of two definitions of statistical solutions of the heat equation (with B.Szafirski and M.Wozniak), Zeszyty Naukowe Uniwersytetu Jagiellonskiego, Prace Matematyczne, Zeszyt 21 (1979), 71-79.
2. A statistical approach to the heat equation, Zeszyty Naukowe Uniwersytetu Jagiellonskiego, Prace Matematyczne, Zeszyt 20 (1979), 111-133.
1. Ultraproducts of higher-order models and nonstandard analysis, Zeszyty Naukowe Uniwersytetu Jagiellonskiego, Prace Matematyczne, Zeszyt 18 (1977), 71-79.