References

  1. Benth F.E. The Gross derivative of generalized random variables. Infin. Dimens. Anal. Quantum Probab. Relat. Top. 1999, 2 (3), 381-396.
  2. Benth F.E., Di Nunno G., Lokka A., Oksendal B., Proske F. Explicit representation of the minimal variance portfolio in markets driven by Levy processes. Math. Finance 2003, 13 (1), 55-72.
  3. Berezansky Yu.M., Sheftel Z.G., Us G.F. Functional Analysis, Vol. 2. Birkhauser Verlag, Basel-Boston-Berlin, 1996. (Russian edition: Vyshcha shkola, Kyiv, 1990.)
  4. Bertoin J. Levy Processes. Cambridge University Press, Cambridge, 1996.
  5. Di Nunno G., Oksendal B., Proske F. Malliavin Calculus for Levy Processes with Applications to Finance. In: Universitext. Springer-Verlag, Berlin, 2009.
  6. Di Nunno G., Oksendal B., Proske F. White noise analysis for Levy processes. J. Funct. Anal. 2004, 206 (1), 109-148. doi: 10.1016/S0022-1236(03)00184-8
  7. Dyriv M.M., Kachanovsky N.A. Operators of stochastic differentiation on spaces of regular test and generalized functions in the Levy white noise analysis. Research Bulletin of National Technical University of Ukraine "Kyiv Polytechnic Institute" 2014, 4, in print.
  8. Dyriv M.M., Kachanovsky N.A. Stochastic integrals with respect to a Levy process and stochastic derivatives on spaces of regular test and generalized functions. Research Bulletin of National Technical University of Ukraine "Kyiv Polytechnic Institute" 2013, 4, 27-30.
  9. Gelfand I.M., Vilenkin N.Ya. Generalized Functions. In: Applications of Harmonic Analysis, 6. Academic Press, New York, London, 1964.
  10. Gihman I.I., Skorohod A.V. Theory of Random Processes, Vol. 2. Nauka, Moscow, 1973.
  11. Holden H., Oksendal B., Uboe J., Zhang T.S. Stochastic Partial Differential Equations. A Modeling, White Noise Functional Approach. In: Probability and Its Applications. Birkhauser, Boston, 1996.
  12. Ito K. Spectral type of the shift transformation of differential processes with stationary increments. Trans. Am. Math. Soc. 1956, 81, 253-263.
  13. Kabanov Yu.M. Extended stochastic integrals. Teorija Verojatnostej i ee Pril. 1975, 20 (4), 725-737.
  14. Kabanov Yu.M., Skorohod A.V. Extended stochastic integrals. In: Proc. School-Symposium ``Theory Stoch. Proc.'', Druskininkai, Lietuvos Respublika, November 25-30, 1974, Inst. Phys. Math., Vilnus, 1975, 123-167.
  15. Kachanovsky N.A. A generalized Malliavin derivative connected with the Poisson- and Gamma-measures. Methods Funct. Anal. Topol. 2003, 9 (3), 213-240.
  16. Kachanovsky N.A. A generalized stochastic derivative on the Kondratiev-type space of regular generalized functions of Gamma white noise. Methods Funct. Anal. Topol. 2006, 12 (4), 363-383.
  17. Kachanovsky N.A. Generalized stochastic derivatives on a space of regular generalized functions of Meixner white noise. Methods Funct. Anal. Topol. 2008, 14 (1), 32-53.
  18. Kachanovsky N.A. Generalized stochastic derivatives on parametrized spaces of regular generalized functions of Meixner white noise. Methods Funct. Anal. Topol. 2008, 14 (4), 334-350.
  19. Kachanovsky N.A. Extended stochastic integrals with respect to a Levy process on spaces of generalized functions. Math. Bull. Shevchenko Sci. Soc. 2013, 10, 169-188.
  20. Kachanovsky N.A. On an extended stochastic integral and the Wick calculus on the connected with the generalized Meixner measure Kondratiev-type spaces. Methods Funct. Anal. Topol. 2007, 13 (4), 338-379.
  21. Kachanovsky N.A. On extended stochastic integrals with respect to Levy processes. Carpathian Math. Publ. 2013, 5 (2), 256-278. doi: 10.15330/cmp.5.2.256-278
  22. Lytvynov E.W. Orthogonal decompositions for Levy processes with an application to the gamma, Pascal, and Meixner processes. Infin. Dimens. Anal. Quantum Probab. Relat. Top. 2003, 6 (1), 73-102.
  23. Meyer P.A. Quantum Probability for Probabilists. In: Lect. Notes in Math., 1538. Springer-Verlag, Berlin, 1993.
  24. Nualart D., Schoutens W. Chaotic and predictable representations for Levy processes. Stochastic Process. Appl. 2000, 90 (1), 109-122.
  25. Protter P. Stochastic Integration and Differential Equations. Springer, Berlin, 1990.
  26. Sato K. Levy Processes and Infinitely Divisible Distributions. In: Cambridge University Studies in Advanced Mathematics, 68. Cambridge University Press, Cambridge, 1999.
  27. Schoutens W. Stochastic Processes and Orthogonal Polynomials. In: Lect. Notes in Statist., 146. Springer-Verlag, 2000.
  28. Skorohod A.V. Integration in Hilbert Space. Springer, New York-Heidelberg, 1974.
  29. Skorohod A.V. On a generalization of a stochastic integral. Teorija Verojatnostej i ee Pril. 1975, 20 (2), 223-238.
  30. Sole J.L., Utzet F., Vives J. Chaos expansions and Malliavin calculus for Levy processes. In: Stoch. Anal. and Appl., Abel Symposium 2, Springer, Berlin, 2007, 595-612.
  31. Surgailis D. On $L^2$ and non-$L^2$ multiple stochastic integration. In: Lect. Notes in Control and Information Sciences, 36, Springer-Verlag, 1981, 212-226.
  32. Ustunel A.S. An Introduction to Analysis on Wiener Space. In: Lect. Notes in Math., Vol. 1610, Springer-Verlag, Berlin, 1995.