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 Electronic Journal of Probability > Vol. 3 (1998) > Paper 7 open journal systems 


On the Approximate Solutions of the Stratonovitch Equation

D. Feyel, Université Evry
A. de La Pradelle, Université Paris VI


Abstract
We present new methods for proving the convergence of the classical approximations of the Stratonovitch equation. We especially make use of the fractional Liouville-valued Sobolev space $W^{r,p}({cal J}_{alpha,p})$. We then obtain a support theorem for the capacity $c_{r,p}$.


Full text: PDF

Pages: 1-14

Published on: May 13, 1998
Bibliography
  1. S.Aida-S.Kusuoka-D.Stroock, On the support of Wiener functionals In Asymptotic problems in Probability Theory; Wiener functionals and Asymptotics; p.3-34. Pitman Research Notes, Longman, 1993 Math Review link
  2. G.Ben Arous-G.Gradinaru, Normes hoeldériennes et support des diffusions CRAS Paris, t.316, série I, no 3, 1993, p.283-286 Math Review link
  3. G.Ben Arous-G.Gradinaru-M.Ledoux, Hoelder norms and the support theorem for diffusions. Ann. Inst. Henri Poincaré, Proba. Stat. 30, no 3, p.415-436, 1994 Math Review link
  4. D.Feyel-A.de La Pradelle, Capacités gaussiennes Ann. Inst. Fourier, t.41, f.1, p.49-76, 1991 Math Review link
  5. D.Feyel-A.de La Pradelle, Fractional integrals and Brownian processes Prépublication 39 de l'Université d'Evry Val d'Essonne, mars 96 Math Review link
  6. D.Feyel-A.de La Pradelle, On fractional Brownian processes To appear in Potential Analysis, 1999
  7. I.Gyoengy-T.Proehle, On the approximation of Stochastic Differential Equations and on Stroock-Varadhan's Support Theorem. Computers Math. Applic. 19, 65-70, 1990 Math Review link
  8. N.Ikeda-S.Watanabe, Stochastic Differential Equations and Diffusion Processes Amsterdam-Oxford-New-York: North Holland; Tokyo: Kodansha, 1981 Math Review link
  9. V.Mackevicius, On the support of the solution of Stochastic Differential Equations. Litovskij Matematikow Rinkings XXXVI (1), 91-98, 1986 Math Review link
  10. A.Millet-M.Sanz-Solé, A simple proof of the support theorem for diffusion processes. Sém. Proba. XXVIII, Lecture Notes in Math. no 1583 p.36-48, 1994. Math Review link
  11. D. Nualart, The Malliavin calculus and related topics. Springer-Verlag, 1995 Math Rev link
  12. J.Ren, Analyse quasi-sûre des équations différentielles stochastiques Bull. Soc. Math.,2ème série, 114, p.187-213, 1990 Math Review link
  13. S.G.Samko, A.A.Kilbas, O.I.Marichev, Fractional Integrals and Derivatives (Theory and Applications). Gordon and Breach Science Publishers, 1987 (976 pages Math Review link
  14. D.W.Stroock-SRS.Varadhan, On the Support of Diffusion Processes with Applications to the strong maximum Principle. Proc. sixth Berkeley Symp. Math. Stat. rob. 3, 333-359, Univ. California Press, Berkeley, 1972 Math Review link
















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Electronic Journal of Probability. ISSN: 1083-6489