References

  1. Benth F.E., Di Nunno G., Løkka A., Øksendal B., Proske F. Explicit representation of the minimal variance portfolio in markets driven by Lévy processes. Math. Finance 2003, 13 (1), 55-72. doi: 10.1111/1467-9965.t01-1-00005
  2. Berezansky Yu.M., Kondratiev Yu.G. Spectral methods in infinite-dimensional analysis. In: Mathematical physics and applied mathematics, 12 (1-2). Kluwer Academic Publishers, Dordrecht, 1995.
  3. Berezansky Yu. M., Sheftel Z.G., Us G.F. Functional analysis. In: Ball J.A., Böttcher A., Dym H. (Eds.) Operator theory: advances and applications, 85 (1). Birkhäuser Verlag, Basel, 1996.
  4. Di Nunno G., Øksendal B., Proske F. Malliavin calculus for Lévy processes with applications to finance. In: Axler S., Casacuberta C., MacIntyre A. Universitext. Springer-Verlag, Berlin, 2009.
  5. Di Nunno G., Øksendal B., Proske F. White noise analysis for Lévy processes. J. Funct. Anal. 2004, 206 (1), 109-148. doi: 10.1016/S0022-1236(03)00184-8
  6. Dyriv M.M., Kachanovsky N.A. On operators of stochastic differentiation on spaces of regular test and generalized functions of Lévy white noise analysis. Carpathian Math. Publ. 2014, 6 (2), 212-229. doi: 10.15330/cmp.6.2.212-229
  7. Dyriv M.M., Kachanovsky N.A. Operators of stochastic differentiation on spaces of regular test and generalized functions in the Lévy white noise analysis. KPI Sci. News 2014, 4, 36-40.
  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. KPI Sci. News 2013, 4, 27-30.
  9. Frei M.M., Kachanovsky N.A. Some remarks on operators of stochastic differentiation in the Lévy white noise analysis. Methods Funct. Anal. Topology 2017, 23 (4), 320-345.
  10. Hida T. Analysis of Brownian Functionals. In: Carleton mathematical lecture notes, Vol. 13. Carleton University, Ottava, 1975.
  11. Holden H., Øksendal B., Uboe J., Zhang T. Stochastic partial differential equations: a modeling, white noise functional approach. Birkhäuser, Boston, 1996.
  12. Itô K. Spectral type of the shift transformation of differential processes with stationary increments. Trans. Amer. Math. Soc. 1956, 81 (1), 253-263. doi: 10.1090/S0002-9947-1956-0077017-0
  13. Kabanov Yu.M., Skorohod A.V. Extended stochastic integrals. In: Proc. School-Seminar "Theory of Random Procesess", Druskininkai, Lietuvos Respublika, November 25-30, 1974, Inst. Phys. Math., Vilnius, 1975, 123-167. (in Russian)
  14. Kachanovsky N.A. An extended stochastic integral and a Wick calculus on parametrized Kondratiev-type spaces of Meixner white noise. Infin. Dimens. Anal. Quantum Probab. Relat. Top. 2008, 11 (4), 541-564. doi: 10.1142/S0219025708003270
  15. Kachanovsky N.A. Extended stochastic integrals and Wick calculus on spaces of regular generalized functions connected with Gamma measure. Ukrainian Math. J. 2005, 57 (8), 1214-1248. doi: 10.1007/s11253-005-0258-8
  16. Kachanovsky N.A. Extended stochastic integrals with respect to a Lévy process on spaces of generalized functions. Math. Bull. Shevchenko Sci. Soc. 2013, 10, 169-188.
  17. Kachanovsky N.A. On extended stochastic integrals with respect to Lévy processes. Carpathian Math. Publ. 2013, 5 (2), 256-278. doi: 10.15330/cmp.5.2.256-278
  18. Kachanovsky N.A. Operators of stochastic differentiation on spaces of nonregular generalized functions of Lévy white noise analysis. Carpathian Math. Publ. 2016, 8 (1), 83-106. doi: 10.15330/cmp.8.1.83-106
  19. Kachanovsky N.A. Operators of stochastic differentiation on spaces of nonregular test functions of Lévy white noise analysis. Methods Funct. Anal. Topology 2015, 21 (4), 336-360.
  20. Kachanovsky N.A., Tesko V.A. Stochastic integral of Hitsuda-Skorokhod type on the extended Fock space. Ukrainian Math. J. 2009, 61 (6), 873-907. doi: 10.1007/s11253-009-0257-2
  21. Kondratiev Yu.G. Generalized functions in problems of infinite-dimensional analysis. Ph. D. Thesis. Kyiv, 1978. (in Russian)
  22. Kondratiev Yu.G., Leukert P., Streit L. Wick calculus in Gaussian analysis. Acta Appl. Math. 1996, 44 (3), 269-294.
  23. Lytvynov E. Orthogonal decompositions for Lévy processes with an application to the gamma, Pascal, and Meixner processes. Infin. Dimens. Anal. Quantum Probab. Relat. Top. 2003, 6 (1), 73-102. doi: 10.1142/S0219025703001031
  24. Nualart D., Schoutens W. Chaotic and predictable representations for Lévy processes. Stochastic Process. Appl. 2000, 90 (1), 109-122. doi: 10.1016/S0304-4149(00)00035-1
  25. Schoutens W. Stochastic Processes and Orthogonal Polynomials. In: Bickel P., Diggle P. (Eds.) Lecture notes in statistics, 146 (1). Springer-Verlag, New York, 2000.
  26. Skorohod A.V. Integration in Hilbert Space. Springer-Verlag, New York and Heidelberg, 1974. (translation of Skorohod A.V. Integration in Hilbert Space. Nauka, Moskow, 1974.(in Russian))
  27. Skorohod A.V. On a generalization of a stochastic integral. Theory Probab. Appl. 1976, 20 (2), 219-233. (translation of Teor. Veroyatn. Primen. 1975, 20 (2), 223-238. (in Russian))
  28. Solé J.L., Utzet F., Vives J. Chaos expansions and Malliavin calculus for Lévy processes. In: Benth F.E., Di Nunno G. (Eds.) Stochastic analysis and applications. Abel symposia, 2. Springer, Heidelberg, 2007, 595-612.
  29. Surgailis D. On $L^2$ and non-$L^2$ multiple stochastic integration. In: Arató M., Vermes D. Stochastic differential systems. Lecture notes in control and information sciences, 36. Springer-Verlag., Heidelberg, 1981, 212-226. doi: 10.1007/BFb0006424
  30. Vershik A.M., Tsilevich N.V. Fock factorizations and decompositions of the $L^2$ spaces over general Lévy processes. Russian Math. Surveys 2003, 58 (3), 427-472. doi: 10.1070/RM2003v058n03ABEH000627

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