On Generalized Regular Stochastic Differential Delay Systems with Time Invariant Coefficients

REFERENCES

• Alabert , A. , and Ferrante , M. 2004 . Linear stochastic differential-algebraic equations with constant coefficients . Electronic Communications in Probability 11 : 316 – 335 .
   Web of Science ®Google Scholar
• Alòs , E. , Mazet , O. , and Nualart , D. 2001 . Stochastic calculus with respect to fractional Brownian motion with Hurst parameter lesser than 1/2 . Stochastic Processes and Applications 86 : 121 – 139 .
   Google Scholar
• Baker , C.T.H. , Paul , C.A.H. , and Willé , D.R. 1995 . A bibliography on numerical solution of delay differential equations . Numerical Analytical Report No. 269 . Department of Mathematics, University of Manchester , U.K .
   Google Scholar
• Bell , D.R. , and Mohammed , S.E.A. 1991 . The Malliavin calculus and stochastic delay equations . Journal of Functional Analysis 99 ( 1 ): 75 – 99 .
   Web of Science ®Google Scholar
• Bellman , R. , and Cooke , K.L. 1963 . Differential-Difference Equations . Academic Press , New York .
   Google Scholar
• Borodin , N.A. , and Salminen , P. 2002 . Handbook of Brownian Motion – Facts and Formulae. , 2nd ed. , Birkhäuser Verlag , Basel, Switzerland .
   Google Scholar
• Campbell , S.L. 1980/1982 . Singular Systems of Differential Equations . Pitman , San Francisco , CA (Vol. 1 , 1980 ; Vol. 2, 1982 ).
   Google Scholar
• Dai , L. 1989 . Singular Control Systems . Springer-Verlag , Berlin .
   Google Scholar
• Dawson , D. 1970 . Generalized stochastic integrals and equations . Transactions of the American Mathematical Society 147 : 473 – 506 .
   Google Scholar
• Descreusefond , L. , and Üstünel , A.S. 1995 . Application du calcul de variations stochastique au mouvement brownien fractionnaire . C. R. Acad. Sci. Paris Sér. I Math. 321 ( 12 ): 1605 – 1608 .
   Google Scholar
• Driver , R.D. 1977 . Ordinary and Delay Differential Equations . Springer-Verlag , New York .
   Google Scholar
• Duncan , T.E. , Hu , Y.Z. , and Pasik-Duncan , B. 2000 . Stochastic calculus for fractional Brownian motion. I. Theory . SIAM Journal of Control Optimization 38 : 582 – 612 .
   Web of Science ®Google Scholar
• Elsgolts , L.E. 1966 . Introduction to the Theory of Differential Equations with Deviating Arguments . Holden-Day , San Francisco .
   Google Scholar
• Fernique , X. 1967 . Processus linéaires, processus generalizes . Annales de l'Institut Fourier (Grenoble) 17 : 1 – 92 .
   Google Scholar
• Forney , G.D. 1975 . Minimal bases of rational vector spaces with application to multivariable systems . SIAM Journal of Control 13 : 493 – 520 .
   Web of Science ®Google Scholar
• Gantmacher , R.F. 1977 . The Theory of Matrices . Chelsea , New York .
   Google Scholar
• Gel'fand , M.I. , and Vilenkin , Ja.N. 1961 . Generalized Functions , Vol. 4 : Some Applications of Harmonic Analysis . Fizmatgiz , Moscow ; [English translation] , Academic Press , New York , 1964 .
   Google Scholar
• Hale , J.K. 1977 . Theory of Functional Differential Equations . Springer-Verlag , New York .
   Google Scholar
• Hu , Y.Z. , and Øksendal , B. 2003 . Fractional white noise calculus and applications to finance . Infinite Dimensional Analysis, Quantum Probability and Related Topics 6 : 1 – 32 .
   Web of Science ®Google Scholar
• Hu , Y.Z. 2005 . Integral transformations and anticipative calculus for fractional Brownian motions . Memoirs of the American Mathematical Society , Vol. 175 , Number 825 , Providence , RI .
   Google Scholar
• Kalogeropoulos , G.I. 1985. Matrix Pencils and Linear Systems. Ph.D. Thesis, City University , London.
   Google Scholar
• Kalogeropoulos , G.I. , and Stratis , I.G. 1999 . On generalized linear regular delay systems . Journal of Mathematical Analysis and Applications 237 : 505 – 514 .
   Web of Science ®Google Scholar
• Kanwal , R.P. 2004 . Generalized Functions: Theory and Applications. . , 3rd ed , Birkhäuser , Boston .
   Google Scholar
• Karcanias , N. 1979 . Matrix pencil approach to geometric systems theory . Proceedings of the IEE 126 : 585 – 590 .
   Google Scholar
• Karcanias , N. , and Hayton , G.E. 1981 . Generalized Autonomous Differential Systems, Algebraic Duality, and Geometric Theory . In Proceedings, IFAC VIII , Triennial World Congress , Kyoto, Japan .
   Google Scholar
• Kunkel , P. , and Mehrmann , V. 2006 . Differential-Algebraic Equations . European Mathematical Society , Zürich .
   Google Scholar
• Kuo , H.H. 1975 . Gaussian Measures in Banach Spaces . Springer-Verlag , Berlin .
   Google Scholar
• Kytagias , D. 1993 . An Algorithmic Method of Computation of the Reduced Set of Quadratic Plücker Relations and Applications in Feedback Problems of Regular and Singular Control Systems . Ph.D. Thesis , University of Athens , Greece .
   Google Scholar
• Mohammed , S.E.A. 1984 . Stochastic Functional Differential Equations . Volume 99 of Research Notes in Mathematics . Pitman (Advanced Publishing Program) , Boston .
   Google Scholar
• Mohammed , S.E.A. 1998 . Stochastic differential systems with memory: Theory, examples and applications . In: Stochastic Analysis and Related Topics VI. The Geilo Workshop, 1996 , Decreusefond , L. , Gjerde , J. Øksendal , B. , and Ustunel , A.S. (eds.), Birkhäuser , Geilo, Norway , pp. 1 – 77 .
   Google Scholar
• Nualart , D. 2006 . Fractional Brownian motion: stochastic calculus and applications . International Congress of Mathematicians. European Mathematical Society, Zürich 3 : 1541 – 1562 .
   Google Scholar
• Schwartz , L. 1966 . Théorie Des Distributions . Publ. Inst. Math. Univ. Strasbourg, Nos. 9, 10 , Hermann , Paris .
   Google Scholar
• Urbanik , K. 1957 . Generalized stochastic processes . Studia Mathematica 16 : 268 – 234 .
   Google Scholar
• Urbanik , K. 1958 . Local characteristics of generalized stochastic processes . Studia Mathematica 18 : 199 – 266 .
   Google Scholar
• Van Dooren , P. 1983 . Reducing Subspaces: Definitions, Properties, and Algorithms, Matrix Pencils . Lecture Notes in Mathematics , Vol. 973 , Springer-Verlag , Berlin .
   Google Scholar
• Wei , J. 2004 . Eigenvalue and stability of singular differential delay systems . Journal of Mathematics and Analytical Applications 297 : 305 – 316 .
   Google Scholar
• Wiener , J. 1993 . Generalized Solution of Functional Differential Equations . World Scientific , NJ .
   Google Scholar
• Yan , F. , and Mohammed , S.E.A. 2005 . Stochastic calculus for systems with memory . Stochstic Analysis Applications 23 ( 3 ): 613 – 657 .
   Google Scholar