14
Views
8
CrossRef citations to date
0
Altmetric
Original Articles

Stabilité d'un type élémentaire d'équations diffé rentielles stochastiques à bruits vectoriesl

Pages 205-213 | Received 29 Feb 1980, Published online: 04 Apr 2007

References

  • Chen , K. T. 1957 . Integration of paths, geometric invariants and a generalized Baker- Hausdorff formula . Ann. of Math , 65 : 163 – 178 .
  • Chen , K. T. 1958 . Integration of paths-a faithful representation of paths by noncommutative formal power series . Trans. Amer.. Math. Soc , 89 : 395 – 407 .
  • Chen , K. T. 1977 . Iterated path integrals . Bull. Amer. Math. Soc , 83 : 831 – 879 .
  • Doss , H. 1977 . Liens entre équations différentielles stochastiques et ordinaires . Ann. Inst. H. Poincare , 13 : 99 – 125 . sect. B
  • Fliess , M. 1977 . Intégrates itérées de K. T. Chen, bruit blanc gaussien et filtrage non linéaire . C.R. Acad. Sci. Paris , A284 : 459 – 462 .
  • Fliess , M. 1979 . “ Quelques remarques sur le "paradoxe" de Wong et Zakai; application à l'identification non lineaire ” . In Actes 7eColloque GRETSI Nice
  • Fliess , M. Fonctionnelles causales non linéaires et indéterminées non commutatives . àparaître ,
  • Freedmann et , M. I. and Willems , J.C. 1978 . Smooth representation of systems with differentiated inputs . , IEEE Trans. Automat. Contr , 23 : 16 – 21 .
  • Gantmacher , F. R. 1966 . Théorie des Matrices, t. 2 Paris, Dunod traduit du russe
  • Goodman , R. 1977 . Lifting vector fields to nilpotent Lie groups . J. Math. Pures Appl , 57 : 77 – 86 .
  • Guelfand et , I. M. and Vilenkin , N.Y. 1967 . Les Distributions, t. 4 Paris, Dunod traduit du russe
  • Hida , T. 1975 . White noise analysis and nonlinear filtering problems . Appl. Math. Optim. , 2 : 82 – 89 .
  • Hormander et , L. and Melin , A. 1978 . Free systems of vector fields . Arkiv for Mat , 16 : 83 – 88 .
  • Ibero , M. 1976 . Integrates stochastiques multiplicatives et construction de diffusions sur un groupe de Lie . Bull. Sci. Math , 100 : 175 – 191 .
  • Krener et , A. J. and Lobry , C. 1979 . “ The complexity of stochastic differential equations ” . preprint
  • Lobry , C. 1977 . l'identification de processus non linéaiics par des méthodes stochastiques . C.R. Acad. Sci. Paris , A284 : 1473 – 1476 .
  • Lobry , C. 1979 . “ Questions de géométrie dans la théorie des équations différentiellesstochastiques ” . In Rapp. Techn. Math. Appl. Info , , Université Bordeaux I .
  • Marcus , S. I. 1978 . Modeling and analysis of stochastic differential equations driven by point processes . IEEE Trans. Inform. Th , 24 : 164 – 172 .
  • Mckean , H. P. 1969 . Stochastic Integrals , New York : Academic Press .
  • Mcshane , E. J. 1974 . Stochastic Calculus and Stochastic Models , New York : Academic Press .
  • Mcshane , E. J. 1975 . Stochastic differential equations . J. Multivariate Anal , 5 : 121 – 177 .
  • Rothschild et , L. P. and Stein , E.M. 1976 . Hypoelliptic differential operators and nilpotent groups . Acta Math , 137 : 247 – 320 .
  • Stratonovich , K. L. 1966 . Conditional Markov Processes and their Application to the Theory of Optimal Control , Moscou, New York : Traduction anglaise Elsevier . en russe
  • Sussmann , H. J. 1976 . “ On generalized inputs and white noise, Proc ” . In 15th IEEE Conf. Decision Control Clearwater, FL
  • Sussmann , H. J. 1978 . On the gap between deterministic and stochastic ordinary differential equations . Ann. Prob , 6 : 19 – 41 .
  • Wong , E. 1971 . Stochastic Processes in Information and Dynamical Systems , New York : McGraw-Hill .
  • Wong et , E. and Zakai , M. 1965 . On the relation between ordinary and stochastic differential equations . Int. J. Engin. Sci , 3 : 213 – 229 .
  • Yamato , Y. 1979 . Stochastic differential equations and nilpotent Lie algebras . Z. Wahrscheinlichkeitstheorie ver.Geb , 47 : 213 – 229 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.