Free Access
Volume 9, June 2005
Page(s) 165 - 184
Published online 15 November 2005
  1. P. Billingsley, Convergence of Probability Measures. Wiley (1968).
  2. A. Bunimovich, H.R. Jauslin, J.L. Lebowitz, A. Pellegrinotti and P. Nielaba, Diffusive energy growth in classical and quantum driven oscillators. J. Stat. Phys. 62 (1991) 793–817. [CrossRef]
  3. L. Coutin and Z. Qian, Stochastic analysis, rough path analysis and fractional Brownian motions. Prob. Th. Related Fields 122 (2002) 108–140. [CrossRef] [MathSciNet]
  4. H. Doss, Liens entre équations différentielles stochastiques et ordinaires. Ann. Inst. H. Poincaré 13 (1977) 99–125.
  5. S.N. Ethier and T.G. Kurtz, Markov processes, characterization and convergence. Wiley, New York (1986).
  6. J.P. Fouque, G. Papanicolaou and R. Sircar, Derivatives in Financial Markets with Stochastic Volatility. Cambridge University Press (2000).
  7. J. Garnier, A multi-scaled diffusion-approximation theorem. Applications to wave propagation in random media. ESAIM: PS 1 (1997) 183–206. [CrossRef] [EDP Sciences]
  8. J. Garnier, Asymptotic behavior of the quantum harmonic oscillator driven by a random time-dependent electric field. J. Stat. Phys. 93 (1998) 211–241. [CrossRef]
  9. J. Garnier, Scattering, spreading, and localization of an acoustic pulse by a random medium, in Three Courses on Partial Differential Equations, E. Sonnendrücker Ed. Walter de Gruyter, Berlin (2003) 71–123.
  10. J. Garnier and R. Marty, Effective pulse dynamics in optical fibers with polarization mode dispersion. Preprint, submitted to Wave Motion.
  11. R.Z. Khasminskii, A limit theorem for solutions of differential equations with random right hand side. Theory Probab. Appl. 11 (1966) 390–406. [CrossRef]
  12. H.J. Kushner, Approximation and weak convergence methods for random processes. MIT Press, Cambridge (1994).
  13. M. Ledoux, T. Lyons and Z. Qian, Lévy area of Wiener processes in Banach spaces. Ann. Probab. 30 (2002) 546–578. [CrossRef] [MathSciNet]
  14. M. Ledoux, Z. Qian and T. Zhang, Large deviations and support theorem for diffusion processes via rough paths. Stoch. Proc. Appl. 102 (2002) 265–283. [CrossRef]
  15. A. Lejay, An introduction to rough paths, in Séminaire de Probabilités XXXVII. Lect. Notes Math. Springer-Verlag (2003).
  16. T. Lyons, Differential equations driven by rough signals. Rev. Mat. Iberoamer. 14 (1998) 215–310.
  17. T. Lyons, Differential equations driven by rough signals (I): an extension of an inequality of L.C. Young. Math. Res. Lett. 1 (1994) 451–464. [CrossRef] [MathSciNet]
  18. T. Lyons and Z. Qian, Flow equations on spaces of rough paths. J. Funct. Anal. 149 (1997) 135–159. [CrossRef] [MathSciNet]
  19. T. Lyons and Z. Qian, System control and rough paths. Oxford Mathematical Monographs. Oxford University Press (2002).
  20. R. Marty, Théorème limite pour une équation différentielle à coefficient aléatoire à mémoire longue. C. R. Acad. Sci. Paris, Ser. I 338 (2004).
  21. A. Messiah, Quantum Mechanics. North Holland, Amsterdam (1962).
  22. D. Middleton, Introduction to statistical communication theory. Mc Graw Hill Book Co., New York (1960).
  23. G. Papanicolaou, Waves in one dimensional random media, in École d'été de Probabilités de Saint-Flour, P.L. Hennequin Ed. Springer. Lect. Notes Math. (1988) 205–275.
  24. G. Papanicolaou and J.B. Keller, Stochastic differential equations with two applications to random harmonic oscillators and waves in random media. SIAM J. Appl. Math. 21 (1971) 287–305. [CrossRef] [MathSciNet]
  25. G. Papanicolaou and W. Kohler, Asymptotic theory of mixing stochastic ordinary differential equations. Comm. Pure Appl. Math. 27 (1974) 641–668. [CrossRef] [MathSciNet]
  26. G. Papanicolaou, D.W. Stroock and S.R.S.Varadhan, Martingale approach to some limit theorem, in Statistical Mechanics and Dynamical systems, D. Ruelle Ed. Duke Turbulence Conf., Duke Univ. Math. Series III, Part IV (1976) 1–120.
  27. G. Samorodnitsky and M.S. Taqqu, Stable non-Gaussian random processes. Chapman and Hall (1994).
  28. L.I. Schiff, Quantum Mechanics. Mac Graw Hill, New York (1968).
  29. K. Sølna, Acoustic Pulse Spreading in a Random Fractal. SIAM J. Appl. Math. 63 (2003) 1764–1788. [CrossRef] [MathSciNet]
  30. H.J. Sussmann, On the gap between deterministic and stochastic ordinary differential equations. Ann. Prob. 6 (1978) 19–41. [CrossRef] [MathSciNet]

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