{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:32:46Z","timestamp":1787319166054,"version":"build-2736575974"},"reference-count":42,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"7","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2010,1]]},"abstract":"<jats:p>Some new Lyapunov-type theorems for stochastic differential equations of neutral type are proved. It is shown that these theorems simplify an application of Kolmanovskii and Shaikhet's general method of Lyapunov functionals construction for stability investigation of different mathematical models.<\/jats:p>","DOI":"10.1137\/080744165","type":"journal-article","created":{"date-parts":[[2010,7,22]],"date-time":"2010-07-22T18:07:03Z","timestamp":1279822023000},"page":"4481-4499","source":"Crossref","is-referenced-by-count":23,"title":["Some New Aspects of Lyapunov-Type Theorems for Stochastic Differential Equations of Neutral Type"],"prefix":"10.1137","volume":"48","author":[{"given":"L.","family":"Shaikhet","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2010,7,22]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","unstructured":"R. Bellman and K. Cooke,\n                      Differential-Difference Equations\n                      , Academic Press, New York, London, 1963.","DOI":"10.1063\/1.3050672"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1016\/S0378-4754(97)00106-7"},{"key":"R3","first-page":"501","volume":"9","author":"Borne P.","year":"2000","journal-title":"Dynam. Systems Appl.","ISSN":"https:\/\/id.crossref.org\/issn\/1056-2176","issn-type":"print"},{"key":"R4","first-page":"203","volume":"5","author":"Borne P.","year":"1999","journal-title":"in Proceedings of The Third Ukrainian-Scandinavian Conference in Probability Theory and Mathematical Statistics (Kiev, 1999), Theory Stoch. Process."},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1155\/2007\/92959"},{"key":"R6","unstructured":"T. A. Burton,\n                      Volterra Integral and Differential Equations\n                      , Academic Press, New York, 1983."},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2007.01.038"},{"key":"R8","doi-asserted-by":"crossref","unstructured":"J. M. Cushing,\n                      Integro-Differential Equations and Delay Models in Population Dynamics\n                      , Lecture Notes in Biomath. 20, Springer-Verlag, Berlin, 1977.","DOI":"10.1007\/978-3-642-93073-7"},{"key":"R9","doi-asserted-by":"crossref","unstructured":"K. Gopalsamy,\n                      Stability and Oscillations in Delay Differential Equations of Population Dynamics\n                      , Kluwer Academic Publishers, Dordrecht, The Netherlands, 1992.","DOI":"10.1007\/978-94-015-7920-9"},{"key":"R10","unstructured":"A. Halanay,\n                      Differential Equations: Stability, Oscillations, Time Lags\n                      , Academic Press, New York, London, 1966."},{"key":"R11","doi-asserted-by":"crossref","unstructured":"J. K. Hale,\n                      Oscillations in neutral functional differential equations\n                      , in Nonlinear Mechanics (Centro Internaz. Mat. Estivo (C.I.M.E.), I Ciclo, Bressanone, 1972), Edizioni Cremonese, Rome, 1973, pp. 97\u2013111.","DOI":"10.1007\/978-3-642-10976-8_2"},{"key":"R12","doi-asserted-by":"crossref","unstructured":"J. K. Hale,\n                      Theory of Functional Differential Equations\n                      , Springer-Verlag, New York, 1977.","DOI":"10.1007\/978-1-4612-9892-2"},{"key":"R13","doi-asserted-by":"crossref","unstructured":"J. K. Hale and S. M. V. Lunel,\n                      Introduction to Functional Differential Equations\n                      , Springer-Verlag, New York, 1993.","DOI":"10.1007\/978-1-4612-4342-7"},{"key":"R14","doi-asserted-by":"crossref","unstructured":"V. B. Kolmanovskii and A. D. Myshkis,\n                      Applied Theory of Functional Differential Equations\n                      , Kluwer Academic Publishers, Dordrecht, Boston, London, 1992.","DOI":"10.1007\/978-94-015-8084-7"},{"key":"R15","doi-asserted-by":"crossref","unstructured":"V. B. Kolmanovskii and A. D. Myshkis,\n                      Introduction to the Theory and Applications of Functional Differential Equations\n                      , Kluwer Academic Publishers, Dordrecht, The Netherlands, 1999.","DOI":"10.1007\/978-94-017-1965-0"},{"key":"R16","unstructured":"V. B. Kolmanovskii and V. R. Nosov,\n                      Stability of Functional Differential Equations\n                      , Academic Press, New York, 1986."},{"key":"R17","unstructured":"V. B. Kolmanovskii and L. E. Shaikhet,\n                      Control of Systems with Aftereffect\n                      , Transl. Math. Monogr. 157, AMS, Providence, RI, 1996."},{"key":"R18","first-page":"1087","volume":"54","author":"Kolmanovskii V. B.","year":"1993","journal-title":"Avtomat. i Telemekh., no. 7, 1993, pp. 66\u201385 (in Russian); Automat. Remote Control"},{"key":"R19","first-page":"1657","volume":"29","author":"Kolmanovskii V. B.","year":"1993","journal-title":"Differ. Uravn., 29 (1993), pp. 1909\u20131920, 2022 (in Russian); Differential Equations"},{"key":"R20","unstructured":"V. B. Kolmanovskii and L. E. Shaikhet,\n                      New results in stability theory for stochastic functional-differential equations (SFDEs) and their applications\n                      , in Proceedings ofDynamic Systems and Applications, Vol. 1 (Atlanta, 1993), Dynamic, Atlanta, GA, 1994, pp. 167\u2013171."},{"key":"R21","first-page":"1819","volume":"31","author":"Kolmanovskii V. B.","year":"1995","journal-title":"Diff. Uravn., 31 (1995), pp. 1851\u20131857, 1941 (in Russian); Differential Equations"},{"key":"R22","doi-asserted-by":"crossref","unstructured":"V. B. Kolmanovskii and L. E. Shaikhet,\n                      General method of Lyapunov functionals construction for stability investigations of stochastic difference equations\n                      , in Dynamical Systems and Applications, World Sci. Ser. Appl. Anal. 4, World Scientific Publishing, River Edge, NJ, 1995, pp. 397\u2013439.","DOI":"10.1142\/9789812796417_0026"},{"key":"R23","first-page":"1735","volume":"57","author":"Kolmanovskii V. B.","year":"1996","journal-title":"Avtomat. i Telemekh., 1996, no. 12, pp. 58\u201366 (in Russian); Automat. Remote Control"},{"key":"R24","doi-asserted-by":"publisher","DOI":"10.1016\/S0893-9659(01)00143-4"},{"key":"R25","doi-asserted-by":"publisher","DOI":"10.1016\/S0895-7177(02)00168-1"},{"key":"R26","doi-asserted-by":"publisher","DOI":"10.1002\/rnc.846"},{"key":"R27","first-page":"49","volume":"6","author":"Kolmanovskii V. B.","year":"2004","journal-title":"Stab. Control Theory Appl."},{"key":"R28","unstructured":"G. S. Ladde, V. Lakshmikantham, and B. G. Zhang,\n                      Oscillation Theory of Differential Equations with Deviating Arguments\n                      , Marcel Dekker, New York, 1987."},{"key":"R29","unstructured":"M. Malek-Zavarei and M. Jamshidi,\n                      Time Delay Systems: Analysis, Optimization and Applications\n                      , North\u2013Holland Systems Control Ser. 9, North\u2013Holland, Amsterdam, 1988."},{"key":"R30","unstructured":"S.E. A. Mohammed,\n                      Stochastic Functional Differential Equations\n                      , Longman Scientific and Technical, Harlow, UK, 1986."},{"key":"R31","unstructured":"A. D. Myshkis,\n                      General Theory of Differential Equations with Delay\n                      , Transl. Math. Monogr. 55, AMS, Providence, RI, 1951."},{"key":"R32","doi-asserted-by":"publisher","DOI":"10.1016\/S0898-1221(04)90111-3"},{"key":"R33","first-page":"248","volume":"2","author":"Shaikhet L. E.","year":"1996","journal-title":"Theory Stoch. Process."},{"key":"R34","doi-asserted-by":"publisher","DOI":"10.1016\/S0893-9659(97)00045-1"},{"key":"R35","first-page":"3","volume":"1","author":"Shaikhet L. E.","year":"1998","journal-title":"Stab. Control Theory Appl."},{"key":"R36","doi-asserted-by":"publisher","DOI":"10.1155\/S1687183904308022"},{"key":"R37","doi-asserted-by":"publisher","DOI":"10.1016\/j.matcom.2004.03.006"},{"key":"R38","doi-asserted-by":"publisher","DOI":"10.1142\/S0219493705001377"},{"key":"R39","doi-asserted-by":"publisher","DOI":"10.1155\/DDNS.2005.215"},{"key":"R40","doi-asserted-by":"publisher","DOI":"10.1111\/j.1934-6093.2006.tb00255.x"},{"key":"R41","first-page":"235","volume":"17","author":"Shaikhet L. E.","year":"2008","journal-title":"Dynam. Systems Appl.","ISSN":"https:\/\/id.crossref.org\/issn\/1056-2176","issn-type":"print"},{"key":"R42","unstructured":"V. Volterra,\n                      Lesons sur la theorie mathematique de la lutte pour la vie\n                      , Gauthier-Villars, Paris, 1931."}],"container-title":["SIAM Journal on Control and Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/080744165","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T12:45:54Z","timestamp":1787316354000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/080744165"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,1]]},"references-count":42,"journal-issue":{"issue":"7","published-print":{"date-parts":[[2010,1]]}},"alternative-id":["10.1137\/080744165"],"URL":"https:\/\/doi.org\/10.1137\/080744165","relation":{},"ISSN":["0363-0129","1095-7138"],"issn-type":[{"value":"0363-0129","type":"print"},{"value":"1095-7138","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,1]]}}}