White noise calculus in applications to stochastic equations in Hilbert spaces
Contemporary Mathematics. Fundamental Directions, Proceedings of the Crimean autumn mathematical school-symposium, Tome 53 (2014), pp. 30-63.

Voir la notice de l'article provenant de la source Math-Net.Ru

@article{CMFD_2014_53_a1,
     author = {I. V. Melnikova and M. A. Alshanskiy},
     title = {White noise calculus in applications to stochastic equations in {Hilbert} spaces},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {30--63},
     publisher = {mathdoc},
     volume = {53},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2014_53_a1/}
}
TY  - JOUR
AU  - I. V. Melnikova
AU  - M. A. Alshanskiy
TI  - White noise calculus in applications to stochastic equations in Hilbert spaces
JO  - Contemporary Mathematics. Fundamental Directions
PY  - 2014
SP  - 30
EP  - 63
VL  - 53
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMFD_2014_53_a1/
LA  - ru
ID  - CMFD_2014_53_a1
ER  - 
%0 Journal Article
%A I. V. Melnikova
%A M. A. Alshanskiy
%T White noise calculus in applications to stochastic equations in Hilbert spaces
%J Contemporary Mathematics. Fundamental Directions
%D 2014
%P 30-63
%V 53
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMFD_2014_53_a1/
%G ru
%F CMFD_2014_53_a1
I. V. Melnikova; M. A. Alshanskiy. White noise calculus in applications to stochastic equations in Hilbert spaces. Contemporary Mathematics. Fundamental Directions, Proceedings of the Crimean autumn mathematical school-symposium, Tome 53 (2014), pp. 30-63. http://geodesic.mathdoc.fr/item/CMFD_2014_53_a1/

[1] Biagini F., Øksendal B., “A general stochastic integral approach to insider trading”, Appl. Math. Optim., 52:4 (2005), 167–181 | DOI | MR | Zbl

[2] Buckdahn R., Anticipating linear stochastic differential equations, Springer, 1989 | MR

[3] Clément Ph., Heijmans H. J. A. M., Angenent S., van Duijn C. J., de Pagter B., One-parameter semigroups, North-Holland, Amsterdam etc., 1987 | MR

[4] Da Prato G., Stochastic evolution equations by semigroup methods, Center de Recerca Matematica, Barcelona, 1997

[5] Da Prato G., Zabczyk J., Stochastic equations in infinite dimensions, Cambridge Univ. Press., Cambridge, 1992 | MR | Zbl

[6] Deck Th., Potthoff J., Våge G., “A rewiev of white noise analysis from a probabilistic standpoint”, Acta Appl. Math., 48:1 (1997), 91–112 | DOI | MR | Zbl

[7] DiNunno G., Øksendal B., Proske F., Malliavin calculus for Lévy processes with applications to finance, Springer, Berlin–Heidelberg, 2009 | MR

[8] Esunge J., “A class of anticipating linear stochastic differential equations”, Commun. Stoch. Anal., 3:1 (2009), 155–164 | MR

[9] Fattorini H. O., The Cauchy problem, Reading. Mass. etc., Addison–Wesley, 1993 | MR

[10] Filinkov A., Sorensen J., “Differential equations in spaces of abstract stochastic distributions”, Stoch. Stoch. Rep., 72:3–4 (2002), 129–173 | DOI | MR | Zbl

[11] Filipović D., Term-structure models. A graduate course., Springer, Berlin, 2009 | MR

[12] Gawarecki L., Mandrekar V., Stochastic differential equations in infinite dimensions with applications to stochastic partial differential equations, Springer–Verlag, Berlin–Heidelberg, 2011 | MR | Zbl

[13] Hida T., Analysis of Brownian functionals, Carleton Univ., Ottawa, 1975 | MR | Zbl

[14] Hille E., Phillips R. S., Functional analysis and semigroups, AMS, Providence, 1957 | Zbl

[15] Holden H., Øksendal B., Uboe J., Zhang T., Stochastic partial differential equations. A modelling, white noise functional approach, Birkhauser, Basel, 1996 | MR | Zbl

[16] Hu Y., Øksendal B., “Optimal smooth portfolio selection for an insider”, J. Appl. Probab., 44:3 (2007), 742–752 | DOI | MR

[17] Huang Z., Yan J., Introduction to infinite dimensional stochastic analysis, Kluver Academic Publishers, Dordrecht, 2000 | MR

[18] Ichikawa A., “Stability of semilinear stochastic evolution equations”, J. Math. Anal. App., 90 (1982), 12–44 | DOI | MR | Zbl

[19] Ichikawa A., “Semilinear stochastic evolution equations: boundedness, stability and invariant measures”, Stochastics, 12 (1984), 1–39 | DOI | MR | Zbl

[20] Kondratiev Yu. G., Streit L., “Spaces of white noise distribution: constructions, descriptions, applications. I”, Rep. Math. Phys., 33 (1993), 341–366 | DOI | MR

[21] Kuo H. H., White noise distribution theory, CRC Press, Boca Raton, 1996 | MR | Zbl

[22] Kubo I., Takenaka S., “Calculus on Gaussian white noise. I”, Proc. Japan Acad. Ser. A Math. Sci., 56A (1980), 376–380 | DOI | MR | Zbl

[23] Kubo I., Takenaka S., “Calculus on Gaussian white noise. II”, Proc. Japan Acad. Ser. A Math. Sci., 56A (1980), 411–416 | DOI | MR | Zbl

[24] Kubo I., Takenaka S., “Calculus on Gaussian white noise. III”, Proc. Japan Acad. Ser. A Math. Sci., 57A (1981), 433–437 | DOI | MR | Zbl

[25] Kubo I., Takenaka S., “Calculus on Gaussian white noise. IV”, Proc. Japan Acad. Ser. A Math. Sci., 58A (1982), 186–189 | DOI | MR | Zbl

[26] Léon J. A., Protter P., “Some formulas for anticipative Girsanov transformations”, Chaos expansions, multiple Wiener-Itô integrals and their applications, 1994, 267–291, CRC Press, Boca Raton | MR | Zbl

[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., 280, Suppl. 1 (2013), 134–150 | DOI

[28] Musiela M., Rutkowski M., Martingale methods in financial modelling, Springer, Berlin, 2005 | MR | Zbl

[29] Nualart D., Pardoux E., “Stochastic calculus with anticipating integrands”, Probab. Theory Related Fields, 78 (1988), 535–581 | DOI | MR | Zbl

[30] Obata N., White noise calculus and Fock space, Springer, Berlin, 1994 | MR | Zbl

[31] Øksendal B., “A universal optimal consumption rate for an insider”, Math. Finance, 16:1 (2006), 119–129 | DOI | MR

[32] Pazy A., Semigroups of linear operators and applications to partial differential equations, Springer, New York, 1983 | MR | Zbl

[33] Shreve S. E., Stochastic calculus for finance. II. Continuous-time models, Springer, New York, 2004 | MR

[34] Stroock D. W., Varadhan S. R. S., Multidimensional diffusion processes, Springer, Berlin–Heidelberg–New York, 1979 | MR | Zbl

[35] Wiener N., “Differential space”, J. Math. Phys. (M.I.T.), 2 (1923), 131–174