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Central limit theorems and random currents

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Stochastic Differential Systems

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 78))

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References

  1. V. A. Arnold and A. Avez, Problémes ergodiques de la méchanique classique, Paris, 1967.

    Google Scholar 

  2. A. Bensoussan, J. L. Lions and G. C. Papanicolaou, Asymptotic analysis for periodic structure, North-Holland, 1978.

    Google Scholar 

  3. R. Bhattacharyan, A central limit theorem for diffusions with periodic coefficients, Ann. Prob., 13 (1985), 385–396.

    Google Scholar 

  4. L. A. Bunimovich and Ya. G. Sinai, Statistical properties of Lorentz gas with periodic configuration of scatterers, Comm. Math. Phys., 78 (1981), 479–497.

    Google Scholar 

  5. P. E. Conner, The Neumann's problem for differential forms on Riemannian manifolds, Memoirs of the Amer. Math. Soc., 20 (1956).

    Google Scholar 

  6. G. de Rham, Differentiable manifolds, Springer, 1984.

    Google Scholar 

  7. I. M. Gel'fand and S. V. Formin, Geodesic flow on manifold of constant negative curvature, Uspehi Mat. Nauk, 47 (1952), 118–137, (Amer. Math. Soc. Transl. Vol.2 (1955), 49–67).

    Google Scholar 

  8. I. M. Gel'fand and I. I. Pyatecki-Šapiro, A theorem of Poincaré, Dokl. Akad. Nauk, 127 (1959), 490–493.

    Google Scholar 

  9. I. M. Gel'fand and N. Ya. Vilenkin, Generalized functions, Vol.4, Academic Press, 1964.

    Google Scholar 

  10. N. Ikeda and S. Manabe, Stochastic integral of differential forms and its applications, Stochastic Analysis, ed. by A. Friedman and M. Pinsky, 175–185, Academic Press, 1978.

    Google Scholar 

  11. N. Ikeda and S. Watanabe, Stochastic differential equations and diffusion processes, Kodanasha/North-Holland, 1981.

    Google Scholar 

  12. K. Itô, Foundation of stochastic differential equations in infinite dimensional spaces, CBMS-NSF, Regional Conference Series in Applied Mathematics, 1984.

    Google Scholar 

  13. S. Itô, Foundamental solutions of parabolic differential equations and boundary value problems, Jap. J. Math., 20 (1957), 55–102.

    Google Scholar 

  14. H. Kumano-go, Pseudo-differential operators, MIT Press, 1981.

    Google Scholar 

  15. S. Manabe, Stochastic intersection number and homological behaviors of diffusion processes on Riemannian manifolds, Osaka Jour. Math., 19 (1982), 429–457.

    Google Scholar 

  16. M. Nagasawa, The adjoint process of a diffusion with reflecting barrier, Kodai Math. Seminar Reports, 13 (1961), 235–248.

    Google Scholar 

  17. S. Nakao, Stochastic calculus for continuous additive functionals of zero energy, Z. Wahr. verw Geb., 68 (1985), 557–578.

    Google Scholar 

  18. Y. Ochi, Limit theorems for a class of diffusion processes, to appear in "Stochastics".

    Google Scholar 

  19. Y. Ochi, Limit theorems for diffusion processes on compact manifolds, to appear in "Stochastic Processes and their Applications", (Abstract of the talk at 15-th Conference on Stochastic Processes and their Applications of Bernoulli Society for Math. Statist. and Prob.).

    Google Scholar 

  20. G. C. Papanicolaou, D. Stroock and S. R. S. Varadhan, Martingale approach to some limit theorems, 1976 Duke Turbulence Conference, Duke Univ. Math. Series III, 1977.

    Google Scholar 

  21. G. C. Papanicolaou and S. R. S. Varadhan, Diffusions with random coefficients, Statist. and Prob.: Essays in Honor of C. R. Rao, ed. by G. Kallianpur, P. R. Krishnaiah and J. K. Glosh, 547–552, North-Holland, 1982.

    Google Scholar 

  22. G. C. Papanicolaou and S. R. S. Varadhan, Boundary value problems with rapidly oscillating random coefficients, Colloquia Mathematica Societaties, János Bolyai: ed. by J. Fritz, Lebowitz and D. Szász, 1981.

    Google Scholar 

  23. M. Ratner, The central limit theorem for geodesic flows on n-dimensional manifolds of negative curvature, Israel J. Math., 16 (1973), 181–197.

    Google Scholar 

  24. Ya. G. Sinai, The central limit theorem for geodesic flows on manifolds of constant negative curvature, Soviet Math. Dokl., 1 (1960), 983–987.

    Google Scholar 

  25. H. Tanaka, Homogenization of diffusion processes with boundary conditions, Stochastic Analysis and Applications, ed. by M. Pinsky, 411–437, Marcel Dekker, 1984.

    Google Scholar 

  26. H. Watanabe, Potential operator of a recurrent strong Feller process in the strict sense and boundary value problem, J. Math. Soc. Japan, 16 (1964), 83–95.

    Google Scholar 

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Norbert Christopeit Kurt Helmes Michael Kohlmann

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© 1986 Springer-Verlag

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Ikeda, N., Ochi, Y. (1986). Central limit theorems and random currents. In: Christopeit, N., Helmes, K., Kohlmann, M. (eds) Stochastic Differential Systems. Lecture Notes in Control and Information Sciences, vol 78. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0041163

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  • DOI: https://doi.org/10.1007/BFb0041163

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16228-5

  • Online ISBN: 978-3-540-39767-0

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