Preview
Unable to display preview. Download preview PDF.
References
V. A. Arnold and A. Avez, Problémes ergodiques de la méchanique classique, Paris, 1967.
A. Bensoussan, J. L. Lions and G. C. Papanicolaou, Asymptotic analysis for periodic structure, North-Holland, 1978.
R. Bhattacharyan, A central limit theorem for diffusions with periodic coefficients, Ann. Prob., 13 (1985), 385–396.
L. A. Bunimovich and Ya. G. Sinai, Statistical properties of Lorentz gas with periodic configuration of scatterers, Comm. Math. Phys., 78 (1981), 479–497.
P. E. Conner, The Neumann's problem for differential forms on Riemannian manifolds, Memoirs of the Amer. Math. Soc., 20 (1956).
G. de Rham, Differentiable manifolds, Springer, 1984.
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).
I. M. Gel'fand and I. I. Pyatecki-Šapiro, A theorem of Poincaré, Dokl. Akad. Nauk, 127 (1959), 490–493.
I. M. Gel'fand and N. Ya. Vilenkin, Generalized functions, Vol.4, Academic Press, 1964.
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.
N. Ikeda and S. Watanabe, Stochastic differential equations and diffusion processes, Kodanasha/North-Holland, 1981.
K. Itô, Foundation of stochastic differential equations in infinite dimensional spaces, CBMS-NSF, Regional Conference Series in Applied Mathematics, 1984.
S. Itô, Foundamental solutions of parabolic differential equations and boundary value problems, Jap. J. Math., 20 (1957), 55–102.
H. Kumano-go, Pseudo-differential operators, MIT Press, 1981.
S. Manabe, Stochastic intersection number and homological behaviors of diffusion processes on Riemannian manifolds, Osaka Jour. Math., 19 (1982), 429–457.
M. Nagasawa, The adjoint process of a diffusion with reflecting barrier, Kodai Math. Seminar Reports, 13 (1961), 235–248.
S. Nakao, Stochastic calculus for continuous additive functionals of zero energy, Z. Wahr. verw Geb., 68 (1985), 557–578.
Y. Ochi, Limit theorems for a class of diffusion processes, to appear in "Stochastics".
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.).
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.
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.
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.
M. Ratner, The central limit theorem for geodesic flows on n-dimensional manifolds of negative curvature, Israel J. Math., 16 (1973), 181–197.
Ya. G. Sinai, The central limit theorem for geodesic flows on manifolds of constant negative curvature, Soviet Math. Dokl., 1 (1960), 983–987.
H. Tanaka, Homogenization of diffusion processes with boundary conditions, Stochastic Analysis and Applications, ed. by M. Pinsky, 411–437, Marcel Dekker, 1984.
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.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1986 Springer-Verlag
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/BFb0041163
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-16228-5
Online ISBN: 978-3-540-39767-0
eBook Packages: Springer Book Archive