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On the Equivalence of Solutions for a Class of Stochastic Evolution Equations in a Banach Space

dc.contributor.authorGórajski, Mariusz
dc.date.accessioned2015-08-18T09:35:44Z
dc.date.available2015-08-18T09:35:44Z
dc.date.issued2014-02-05
dc.identifier.issn1420-8989
dc.identifier.urihttp://hdl.handle.net/11089/11527
dc.descriptionAcknowledgments: The author wishes to thank Professor Anna Chojnowska-Michalik and the referee for many helpful suggestions and comments.pl_PL
dc.description.abstractWe study a class of stochastic evolution equations in a Banach space E driven by cylindrical Wiener process. Three different analytical concepts of solutions: generalised strong, weak and mild are defined and the conditions under which they are equivalent are given. We apply this result to prove existence, uniqueness and continuity of weak solutions to stochastic delay evolution equations. We also consider two examples of these equations in non-reflexive Banach spaces: a stochastic transport equation with delay and a stochastic delay McKendrick equation.pl_PL
dc.language.isoenpl_PL
dc.publisherSpringer Baselpl_PL
dc.relation.ispartofseriesIntegral Equations and Operator Theory;
dc.relation.ispartofseriesIntegral Equations and Operator Theory;78
dc.rightsUznanie autorstwa 3.0 Polska*
dc.rights.urihttp://creativecommons.org/licenses/by/3.0/pl/*
dc.subjectStochastic evolution equations, umd − Banach spacespl_PL
dc.subjectmild solutionspl_PL
dc.subjectweak solutionspl_PL
dc.subjectgeneralised strong solutionspl_PL
dc.subjectstochastic partial differential equations with finite delaypl_PL
dc.titleOn the Equivalence of Solutions for a Class of Stochastic Evolution Equations in a Banach Spacepl_PL
dc.typeArticlepl_PL
dc.page.number451–481pl_PL
dc.contributor.authorAffiliationUniversity of Łódź, Faculty of Economics and Sociology, Department of Econometricspl_PL
dc.referencesBaker, C.T.H., Bocharov, G.A., Rihan, F.A.: A report on the use of delay differential equations in numerical modelling in the biosciences. Numer. Anal. Rep. 343, 146 (1999)pl_PL
dc.referencesBarucci, E., Gozzi, F.: Optimal advertising with a continuum of goods. Ann. Oper. Res. 88, 15–29 (1999)pl_PL
dc.referencesB´atkai, A., Piazzera, S.: Semigroups for Delay Equations, Research Notes in Mathematics 10, A K Peters Ltd., Wellesley, MA (2005)pl_PL
dc.referencesBobrowski, A.: Lord Kelvin’s method of images in semigroup theory. Semigroup Forum 81(3), 435–445 (2010)pl_PL
dc.referencesBrzeźniak, Z., Neerven, J.M.A.M.van : Stochastic convolution in separable Banach spaces and the stochastic linear Cauchy problem. StudiaMath. 143(1), 43– 74 (2000)pl_PL
dc.referencesChojnowska-Michalik, A.: Stochastic differential equations in Hilbert spaces. In: Probability Theory (Papers, VIIth Semester, Stefan Banach Internat. Math. Center, Warsaw, 1976), vol. 5, pp. 53–74. Banach Center Publications (1979)pl_PL
dc.referencesCox, S., Górajski, M.: Vector-valued stochastic delay equations-a semigroup approach. Semigroup Forum 82, 389–411 (2011)pl_PL
dc.referencesCox, S., Veraar, M.: Vector-valued decoupling and the Burkholder–Davis– Gundy inequality. Ill. J. Math. 55(1):343–375 (2011)pl_PL
dc.referencesCrewe, P.: Infinitely delayed stochastic evolution equations in UMD Banach spaces arXiv:1011.2615v1pl_PL
dc.referencesDa Prato, G., Kwapień, S., Zabczyk, J.: Regularity of solutions of linear stochastic equations in Hilbert spaces. Stochastics 23(1), 1–23 (1987)pl_PL
dc.referencesDa Prato, G.; Zabczyk, J.: Stochastic equations in infinite dimensions. In: Encyclopedia of Mathematics and its Applications, vol. 44. Cambridge University Press, Cambridge (1992)pl_PL
dc.referencesDenk, R.; Hieber, M.; Pruss, J.: R-boundedness, Fourier multipliers and problems of elliptic and parabolic type. Mem. Am. Math. Soc. 166(788), viii+114 (2003)pl_PL
dc.referencesEngel, K.; Nagel, R.: One-parameter semigroups for linear evolution equations. In: Graduate Texts in Mathematics, vol. 194. Springer-Verlag, New York (2000)pl_PL
dc.referencesErneux, T.: Applied Delay Differential Equations, Surveys and Tutorials in the Applied Mathematical Sciences, vol. 3. Springer, New York (2009)pl_PL
dc.referencesGarling, D.: Random martingale transform inequalities. In: Probability in Banach spaces 6, Sandbjerg, 1986, Progr. Probab. 20, pp. 101–119. Birkh¨auser Boston, Boston, MA (1990)pl_PL
dc.referencesGórajski, M.: Vector-valued stochastic delay equations—a weak solution and its Markovian representation, arXiv preprint arXiv:1301.5300pl_PL
dc.referencesKalton, N.J.; Weis, L.: The H∞-functional calculus and square function estimates, Manuscript in preparationpl_PL
dc.referencesKunze, M.C.: Martingale problems on Banach spaces, arXiv preprint arXiv:1009.2650 (2012)pl_PL
dc.referencesMao, X.: Stochastic Differential Equations and Their Applications. Horwood Publishing Series in Mathematics & Applications, Horwood, Chichester (1997)pl_PL
dc.referencesMohammed, S.E.A.: Stochastic Functional Differential Equations, Research Notes in Mathematics, vol. 99. Pitman, Boston (1984)pl_PL
dc.referencesvan Neerven, J.M.A.M.: The Adjoint of a Semigroup of Linear Operators, Lecture Notes in Mathematics, vol. 1529. Springer-Verlag, Berlin (1992)pl_PL
dc.referencesvan Neerven, J.M.A.M.: Stochastic Evolution Equations, Notes to the 11th Internet Seminar (2008)pl_PL
dc.referencesvan Neerven, J.M.A.M., Veraar, M., Weis, L.: Stochastic evolution equations in UMD Banach spaces. J. Funct. Anal. 255, 940–993 (2008)pl_PL
dc.referencesvan Neerven, J.M.A.M.; Veraar, M.C.: On the stochastic Fubini theorem in infinite dimensions, in: Stochastic partial differential equations and applications— VII, Lecturer Notes in Pure Applied Mathematics, vol. 245, pp. 323–336. Chapman & Hall/CRC, Boca Raton, FL (2006)pl_PL
dc.referencesvan Neerven, J.M.A.M., Veraar, M.C., Weis, L.: Stochastic integration in UMD Banach spaces. Ann. Probab. 35(4), 1438–1478 (2007)pl_PL
dc.referencesvan Neerven, J.M.A.M., Weis, L.: Stochastic integration of functions with values in a Banach space. Studia Math. 166(2), 131–170 (2005)pl_PL
dc.referencesPeszat, S.; Zabczyk, J.: Stochastic partial differential equations with L´evy noise. In: Encyclopedia of Mathematics and its Applications, vol. 113. Cambridge University Press, Cambridge (2007)pl_PL
dc.referencesQi-Min, Z., Wen-An, L., Zan-Kan, N.: Existence, uniqueness and exponential stability for stochastic age-dependent population. Appl. Math. Comput. 154, 183–201 (2004)pl_PL
dc.referencesVeraar, M.: Stochastic integration in Banach spaces and applications to parabolic evolution equations. ISBN:978-90-9021380-4 (2006)pl_PL
dc.referencesVeraar, M., Zimmerschied, J.: Non-autonomous stochastic Cauchy problems in Banach spaces. Studia Math. 185(1), 1–34 (2008)pl_PL
dc.referencesWebb, G.: Theory of nonlinear age-dependent population dynamics, 89, CRC (1985)pl_PL
dc.contributor.authorEmailmariuszg@math.uni.lodz.plpl_PL
dc.identifier.doi10.1007/s00020-013-2119-4


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