Analiz belogo shuma v prilozheniyakh k stokhasticheskim uravneniyam v gil'bertovykh prostranstvakh

Cover Page

Cite item

Full Text

Abstract

References

  1. Biagini F., Øksendal B. A general stochastic integral approach to insider trading// Appl. Math. Optim. - 2005. - 52, №4. - С. 167-181.
  2. Buckdahn R. Anticipating linear stochastic di erential equations. - Springer, 1989. - С. 18-23.
  3. Cle´ment Ph., Heijmans H. J. A. M., Angenent S., van Duijn C. J., de Pagter B. One-parameter semigroups. - Amsterdam etc.: North-Holland, 1987.
  4. Da Prato G. Stochastic evolution equations by semigroup methods. - Barcelona: Center de Recerca Matematica, 1997.
  5. Da Prato G., Zabczyk J. Stochastic equations in in nite dimensions. - Cambridge: Cambridge Univ. Press., 1992.
  6. Deck Th., Pottho J., V˚age G. A rewiev of white noise analysis from a probabilistic standpoint// Acta Appl. Math. - 1997. - 48, №1. - С. 91-112.
  7. DiNunno G., Øksendal B., Proske F. Malliavin calculus for Le´vy processes with applications to nance. - Berlin-Heidelberg: Springer, 2009.
  8. Esunge J. A class of anticipating linear stochastic di erential equations// Commun. Stoch. Anal. - 2009. - 3, № 1. - С. 155-164.
  9. Fattorini H. O. The Cauchy problem. - Addison-Wesley: Reading. Mass. etc., 1993.
  10. Filinkov A., Sorensen J. Di erential equations in spaces of abstract stochastic distributions// Stoch. Stoch. Rep. - 2002. - 72, № 3-4. - С. 129-173.
  11. Filipovic´ D. Term-structure models. A graduate course. - Berlin: Springer, 2009.
  12. Gawarecki L., Mandrekar V. Stochastic di erential equations in in nite dimensions with applications to stochastic partial di erential equations. - Berlin-Heidelberg: Springer-Verlag, 2011.
  13. Hida T. Analysis of Brownian functionals. - Ottawa: Carleton Univ., 1975.
  14. Hille E., Phillips R. S. Functional analysis and semigroups. - Providence: AMS, 1957.
  15. Holden H., Øksendal B., Ubøe J., Zhang T. Stochastic partial di erential equations. A modelling, white noise functional approach. - Basel: Birkhauser, 1996.
  16. Hu Y., Øksendal B. Optimal smooth portfolio selection for an insider// J. Appl. Probab. - 2007. - 44, №3. - С. 742--752.
  17. Huang Z., Yan J. Introduction to in nite dimensional stochastic analysis. - Dordrecht: Kluver Academic Publishers, 2000.
  18. Ichikawa A. Stability of semilinear stochastic evolution equations// J. Math. Anal. App. - 1982. - 90.- С. 12-44.
  19. Ichikawa A. Semilinear stochastic evolution equations: boundedness, stability and invariant measures// Stochastics. - 1984. - 12. - С. 1-39.
  20. Kondratiev Yu. G., Streit L. Spaces of white noise distribution: constructions, descriptions, applications. I// Rep. Math. Phys. - 1993. - 33. - С. 341-366.
  21. Kuo H.-H. White noise distribution theory. - Boca Raton: CRC Press, 1996.
  22. Kubo I., Takenaka S. Calculus on Gaussian white noise. I// Proc. Japan Acad. Ser. A Math. Sci. - 1980. - 56A. - С. 376-380.
  23. Kubo I., Takenaka S. Calculus on Gaussian white noise. II// Proc. Japan Acad. Ser. A Math. Sci. - 1980. - 56A. - С. 411-416.
  24. Kubo I., Takenaka S. Calculus on Gaussian white noise. III// Proc. Japan Acad. Ser. A Math. Sci. - 1981. - 57A. - С. 433-437.
  25. Kubo I., Takenaka S. Calculus on Gaussian white noise. IV// Proc. Japan Acad. Ser. A Math. Sci. - 1982. - 58A. - С. 186-189.
  26. Le` on J. A., Protter P. Some formulas for anticipative Girsanov transformations// В сб.: «Chaos expansions, multiple Wiener-Itoˆ integrals and their applications». - Boca Raton: CRC Press, 1994. - С. 267-291.
  27. Melnikova I. V., Alshanskiy M. A. The generalized well-posedness of the Cauchy problem for an abstract stochastic equation with multiplicative noise// Proc. Steklov Inst. Math. - 2013. - 280, (Suppl. 1). - С. 134-150.
  28. Musiela M., Rutkowski M. Martingale methods in nancial modelling. - Berlin: Springer, 2005.
  29. Nualart D., Pardoux E. Stochastic calculus with anticipating integrands// Probab. Theory Related Fields. - 1988. - 78. - С. 535-581.
  30. Obata N. White noise calculus and Fock space. - Berlin: Springer, 1994.
  31. Øksendal B. A universal optimal consumption rate for an insider// Math. Finance. - 2006. - 16, №1. - С. 119--129.
  32. Pazy A. Semigroups of linear operators and applications to partial di erential equations. - New York: Springer, 1983.
  33. Shreve S. E. Stochastic calculus for nance. II. Continuous-time models. - New York: Springer, 2004.
  34. Stroock D. W., Varadhan S. R. S. Multidimensional di usion processes. - Berlin-Heidelberg-New York: Springer, 1979.
  35. Wiener N. Di erential space// J. Math. Phys. (M.I.T.). - 1923. - 2. - С. 131-174.

Copyright (c) 2014 Mel'nikova I.V., Al'shanskiy M.A.

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

This website uses cookies

You consent to our cookies if you continue to use our website.

About Cookies