<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE root>
<article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:ali="http://www.niso.org/schemas/ali/1.0/" article-type="research-article" dtd-version="1.2" xml:lang="en"><front><journal-meta><journal-id journal-id-type="publisher-id">Contemporary Mathematics. Fundamental Directions</journal-id><journal-title-group><journal-title xml:lang="en">Contemporary Mathematics. Fundamental Directions</journal-title><trans-title-group xml:lang="ru"><trans-title>Современная математика. Фундаментальные направления</trans-title></trans-title-group></journal-title-group><issn publication-format="print">2413-3639</issn><issn publication-format="electronic">2949-0618</issn><publisher><publisher-name xml:lang="en">Peoples’ Friendship University of Russia named after Patrice Lumumba (RUDN University)</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="publisher-id">33530</article-id><article-categories><subj-group subj-group-type="toc-heading" xml:lang="en"><subject>Articles</subject></subj-group><subj-group subj-group-type="toc-heading" xml:lang="ru"><subject>Статьи</subject></subj-group><subj-group subj-group-type="article-type"><subject>Research Article</subject></subj-group></article-categories><title-group><article-title xml:lang="en">Analiz belogo shuma v prilozheniyakh k stokhasticheskim uravneniyam v gil'bertovykh prostranstvakh</article-title><trans-title-group xml:lang="ru"><trans-title>Анализ белого шума в приложениях к стохастическим уравнениям в гильбертовых пространствах</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author"><name-alternatives><name xml:lang="en"><surname>Mel'nikova</surname><given-names>I. V.</given-names></name><name xml:lang="ru"><surname>Мельникова</surname><given-names>И. В.</given-names></name></name-alternatives><email>Irina.Melnikova@usu.ru</email><xref ref-type="aff" rid="aff1"/></contrib><contrib contrib-type="author"><name-alternatives><name xml:lang="en"><surname>Al'shanskiy</surname><given-names>M. A.</given-names></name><name xml:lang="ru"><surname>Альшанский</surname><given-names>М. А.</given-names></name></name-alternatives><email>mxalsh@gmail.com</email><xref ref-type="aff" rid="aff1"/></contrib></contrib-group><aff-alternatives id="aff1"><aff><institution xml:lang="en"></institution></aff><aff><institution xml:lang="ru">Уральский федеральный университет</institution></aff></aff-alternatives><pub-date date-type="pub" iso-8601-date="2014-12-15" publication-format="electronic"><day>15</day><month>12</month><year>2014</year></pub-date><volume>53</volume><issue-title xml:lang="en">VOL 53, NO (2014)</issue-title><issue-title xml:lang="ru">ТОМ 53, № (2014)</issue-title><fpage>30</fpage><lpage>63</lpage><history><date date-type="received" iso-8601-date="2023-02-10"><day>10</day><month>02</month><year>2023</year></date></history><permissions><copyright-statement xml:lang="en">Copyright ©; 2014, Mel'nikova I.V., Al'shanskiy M.A.</copyright-statement><copyright-statement xml:lang="ru">Copyright ©; 2014, Мельникова И.В., Альшанский М.А.</copyright-statement><copyright-year>2014</copyright-year><copyright-holder xml:lang="en">Mel'nikova I.V., Al'shanskiy M.A.</copyright-holder><copyright-holder xml:lang="ru">Мельникова И.В., Альшанский М.А.</copyright-holder><ali:free_to_read xmlns:ali="http://www.niso.org/schemas/ali/1.0/"/><license><ali:license_ref xmlns:ali="http://www.niso.org/schemas/ali/1.0/">https://creativecommons.org/licenses/by-nc/4.0</ali:license_ref></license></permissions><self-uri xlink:href="https://journals.rudn.ru/CMFD/article/view/33530">https://journals.rudn.ru/CMFD/article/view/33530</self-uri><abstract xml:lang="en"> </abstract><trans-abstract xml:lang="ru"> </trans-abstract></article-meta></front><body></body><back><ref-list><ref id="B1"><label>1.</label><mixed-citation>Biagini F., Øksendal B. A general stochastic integral approach to insider trading// Appl. Math. Optim. - 2005. - 52, №4. - С. 167-181.</mixed-citation></ref><ref id="B2"><label>2.</label><mixed-citation>Buckdahn R. Anticipating linear stochastic di erential equations. - Springer, 1989. - С. 18-23.</mixed-citation></ref><ref id="B3"><label>3.</label><mixed-citation>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.</mixed-citation></ref><ref id="B4"><label>4.</label><mixed-citation>Da Prato G. Stochastic evolution equations by semigroup methods. - Barcelona: Center de Recerca Matematica, 1997.</mixed-citation></ref><ref id="B5"><label>5.</label><mixed-citation>Da Prato G., Zabczyk J. Stochastic equations in in nite dimensions. - Cambridge: Cambridge Univ. Press., 1992.</mixed-citation></ref><ref id="B6"><label>6.</label><mixed-citation>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.</mixed-citation></ref><ref id="B7"><label>7.</label><mixed-citation>DiNunno G., Øksendal B., Proske F. Malliavin calculus for Le´vy processes with applications to  nance. - Berlin-Heidelberg: Springer, 2009.</mixed-citation></ref><ref id="B8"><label>8.</label><mixed-citation>Esunge J. A class of anticipating linear stochastic di erential equations// Commun. Stoch. Anal. - 2009. - 3, № 1. - С. 155-164.</mixed-citation></ref><ref id="B9"><label>9.</label><mixed-citation>Fattorini H. O. The Cauchy problem. - Addison-Wesley: Reading. Mass. etc., 1993.</mixed-citation></ref><ref id="B10"><label>10.</label><mixed-citation>Filinkov A., Sorensen J. Di erential equations in spaces of abstract stochastic distributions// Stoch. Stoch. Rep. - 2002. - 72, № 3-4. - С. 129-173.</mixed-citation></ref><ref id="B11"><label>11.</label><mixed-citation>Filipovic´ D. Term-structure models. A graduate course. - Berlin: Springer, 2009.</mixed-citation></ref><ref id="B12"><label>12.</label><mixed-citation>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.</mixed-citation></ref><ref id="B13"><label>13.</label><mixed-citation>Hida T. Analysis of Brownian functionals. - Ottawa: Carleton Univ., 1975.</mixed-citation></ref><ref id="B14"><label>14.</label><mixed-citation>Hille E., Phillips R. S. Functional analysis and semigroups. - Providence: AMS, 1957.</mixed-citation></ref><ref id="B15"><label>15.</label><mixed-citation>Holden H., Øksendal B., Ubøe J., Zhang T. Stochastic partial di erential equations. A modelling, white noise functional approach. - Basel: Birkhauser, 1996.</mixed-citation></ref><ref id="B16"><label>16.</label><mixed-citation>Hu Y., Øksendal B. Optimal smooth portfolio selection for an insider// J. Appl. Probab. - 2007. - 44, №3. - С. 742--752.</mixed-citation></ref><ref id="B17"><label>17.</label><mixed-citation>Huang Z., Yan J. Introduction to in nite dimensional stochastic analysis. - Dordrecht: Kluver Academic Publishers, 2000.</mixed-citation></ref><ref id="B18"><label>18.</label><mixed-citation>Ichikawa A. Stability of semilinear stochastic evolution equations// J. Math. Anal. App. - 1982. - 90.- С. 12-44.</mixed-citation></ref><ref id="B19"><label>19.</label><mixed-citation>Ichikawa A. Semilinear stochastic evolution equations: boundedness, stability and invariant measures// Stochastics. - 1984. - 12. - С. 1-39.</mixed-citation></ref><ref id="B20"><label>20.</label><mixed-citation>Kondratiev Yu. G., Streit L. Spaces of white noise distribution: constructions, descriptions, applications. I// Rep. Math. Phys. - 1993. - 33. - С. 341-366.</mixed-citation></ref><ref id="B21"><label>21.</label><mixed-citation>Kuo H.-H. White noise distribution theory. - Boca Raton: CRC Press, 1996.</mixed-citation></ref><ref id="B22"><label>22.</label><mixed-citation>Kubo I., Takenaka S. Calculus on Gaussian white noise. I// Proc. Japan Acad. Ser. A Math. Sci. - 1980. - 56A. - С. 376-380.</mixed-citation></ref><ref id="B23"><label>23.</label><mixed-citation>Kubo I., Takenaka S. Calculus on Gaussian white noise. II// Proc. Japan Acad. Ser. A Math. Sci. - 1980. - 56A. - С. 411-416.</mixed-citation></ref><ref id="B24"><label>24.</label><mixed-citation>Kubo I., Takenaka S. Calculus on Gaussian white noise. III// Proc. Japan Acad. Ser. A Math. Sci. - 1981. - 57A. - С. 433-437.</mixed-citation></ref><ref id="B25"><label>25.</label><mixed-citation>Kubo I., Takenaka S. Calculus on Gaussian white noise. IV// Proc. Japan Acad. Ser. A Math. Sci. - 1982. - 58A. - С. 186-189.</mixed-citation></ref><ref id="B26"><label>26.</label><mixed-citation>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.</mixed-citation></ref><ref id="B27"><label>27.</label><mixed-citation>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.</mixed-citation></ref><ref id="B28"><label>28.</label><mixed-citation>Musiela M., Rutkowski M. Martingale methods in  nancial modelling. - Berlin: Springer, 2005.</mixed-citation></ref><ref id="B29"><label>29.</label><mixed-citation>Nualart D., Pardoux E. Stochastic calculus with anticipating integrands// Probab. Theory Related Fields. - 1988. - 78. - С. 535-581.</mixed-citation></ref><ref id="B30"><label>30.</label><mixed-citation>Obata N. White noise calculus and Fock space. - Berlin: Springer, 1994.</mixed-citation></ref><ref id="B31"><label>31.</label><mixed-citation>Øksendal B. A universal optimal consumption rate for an insider// Math. Finance. - 2006. - 16, №1. - С. 119--129.</mixed-citation></ref><ref id="B32"><label>32.</label><mixed-citation>Pazy A. Semigroups of linear operators and applications to partial di erential equations. - New York: Springer, 1983.</mixed-citation></ref><ref id="B33"><label>33.</label><mixed-citation>Shreve S. E. Stochastic calculus for  nance. II. Continuous-time models. - New York: Springer, 2004.</mixed-citation></ref><ref id="B34"><label>34.</label><mixed-citation>Stroock D. W., Varadhan S. R. S. Multidimensional di usion processes. - Berlin-Heidelberg-New York: Springer, 1979.</mixed-citation></ref><ref id="B35"><label>35.</label><mixed-citation>Wiener N. Di erential space// J. Math. Phys. (M.I.T.). - 1923. - 2. - С. 131-174.</mixed-citation></ref></ref-list></back></article>
