Stochastic Integrals and Stochastic Functional Equations

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Previous article Next article Stochastic Integrals and Stochastic Functional EquationsE. J. McShaneE. J. McShanehttps://doi.org/10.1137/0117029PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Garrett Birkhoff and , Gian-Carlo Rota, Ordinary differential equations, Introductions to Higher Mathematics, Ginn and Company, Boston, Mass.-New York-Toronto, 1962vii+318 MR0138810 0102.29901 Google Scholar[2] J. L. Doob, Stochastic processes, John Wiley & Sons Inc., New York, 1953viii+654 MR0058896 0053.26802 Google Scholar[3] Kiyoshi Itô and , Makiko Nisio, On stationary solutions of a stochastic differential equation, J. Math. Kyoto Univ., 4 (1964), 1–75 MR0177456 0131.16402 CrossrefGoogle Scholar[4A] R. L. Stratonovič, A new form of representing stochastic integrals andequations, Vestnik Moskov. Univ. Ser. I Mat. Meh., 1964 (1964), 3–12 MR0160262 Google Scholar[4B] R. L. Stratonovich, A new representation for stochastic integrals and equations, SIAM J. Control, 4 (1966), 362–371 10.1137/0304028 MR0196814 LinkGoogle Scholar[5] L. Tonflli, Sulle equazioni funzionali del tipo di Volterra, Bull. Calcutta Math. Soc., 20 (1928), 31–48 Google Scholar[6] G. Maruyama, Continuous Markov processes and stochastic equations, Rend. Circ. Mat. Palermo (2), 4 (1955), 48–90 MR0071666 0053.40901 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Convergence Theorems in the Sense of Vitali and Lusin for the Itô–Henstock IntegralProceedings of the Singapore National Academy of Science, Vol. 15, No. 01 | 8 March 2021 Cross Ref Stochastic calculus on Fréchet spacesAdvances in Operator Theory, Vol. 6, No. 1 | 23 November 2020 Cross Ref Double Lusin condition and Vitali convergence theorem for the Itô–McShane IntegralAdvances in Operator Theory, Vol. 5, No. 2 | 24 January 2020 Cross Ref Backwards Itô–Henstock’s version of Itô’s formulaAnnals of Functional Analysis, Vol. 11, No. 1 | 1 December 2019 Cross Ref Stochastic functional differential equations with infinite delay: Existence and uniqueness of solutions, solution maps, Markov properties, and ergodicityJournal of Differential Equations, Vol. 262, No. 3 | 1 Feb 2017 Cross Ref A partial history of the early development of continuous-time nonlinear stochastic systems theoryAutomatica, Vol. 50, No. 2 | 1 Feb 2014 Cross Ref On the existence and uniqueness of solutions of McShane type stochastic differential equationsStochastic Analysis and Applications, Vol. 16, No. 2 | 1 Jan 1998 Cross Ref Conformal Martingales in Stochastic MechanicsStochastic Processes and their Applications | 1 Jan 1991 Cross Ref Excursions and Itôcalculus in Nelson’s Stochastic MechanicsRecent Developments in Quantum Mechanics | 1 Jan 1991 Cross Ref Existence, Uniqueness, and Upper Estimates for Solutions of Mcshane Type Stochastic Differential SystemsStochastic Analysis and Applications, Vol. 4, No. 4 | 1 Jan 1986 Cross Ref Chapter 11 Nonlinear stochastic system modelsStochastic Models, Estimation, and Control: Volume 2 | 1 Jan 1982 Cross Ref BibliographyThe Hamilton-Jacobi Equation A Global Approach | 1 Jan 1977 Cross Ref A Stochastic Maximum PrincipleVirginia M. WarfieldSIAM Journal on Control and Optimization, Vol. 14, No. 5 | 18 July 2006AbstractPDF (1607 KB)Stochastic differential equationsJournal of Multivariate Analysis, Vol. 5, No. 2 | 1 Jun 1975 Cross Ref First passage time process of a standard brownian motionScandinavian Actuarial Journal, Vol. 1975, No. 2 | 1 Apr 1975 Cross Ref The digital simulation of stochastic differential equationsIEEE Transactions on Automatic Control, Vol. 19, No. 1 | 1 Feb 1974 Cross Ref STOCHASTIC INTEGRATIONVector and Operator Valued Measures and Applications | 1 Jan 1973 Cross Ref Product integral solutions for hereditary systemsTransactions of the American Mathematical Society, Vol. 181, No. 0 | 1 January 1973 Cross Ref On McShane’s Belated Stochastic IntegralZoran R. Pop-StojanovicSIAM Journal on Applied Mathematics, Vol. 22, No. 1 | 12 July 2006AbstractPDF (549 KB)Chapter 7 Itô Random Integral EquationsRandom Integral Equations | 1 Jan 1972 Cross Ref Volume 17, Issue 2| 1969SIAM Journal on Applied Mathematics223-493 History Submitted:09 January 1968Published online:12 July 2006 InformationCopyright © 1969 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0117029Article page range:pp. 287-306ISSN (print):0036-1399ISSN (online):1095-712XPublisher:Society for Industrial and Applied Mathematics