Abstract.
We prove a functional central limit theorem for diffusions on periodic sub- manifolds of ℝN. The proof is an adaptation of a method presented in [BenLioPap] and [Bha] for proving functional central limit theorems for diffusions with periodic drift vectorfields. We then apply the central limit theorem in order to obtain a recurrence and a transience criterion for periodic diffusions. Other fields of applications could be heat-kernel estimates, similar to the ones obtained in [Lot].
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Aubin, T.: Some nonlinear Problems in Riemannian Geometry. SMM, Springer Berlin, 1998
Bhattacharya, R.: A central limit theorem for diffusions with periodic coefficients. Annals of Probability, 13, 385–396 (1985)
Bensoussan, A., Lions, J.L., Papanicolaou, G.: Asymptotic Analysis for periodic Structures. North-Holland, 1978
Ethier, S., Kurtz, T.: Markov Processes: Characterization and Convergence. John Wiley & Sons, Inc, New-York, 1986
Hsu, E. P.: Stochastic Analysis on Manifolds. AMS Graduate Studies in Mathematics 38, 2001
Jost, J.: Riemannian Geometry and geometric Analysis. 3ed. Universitext, Springer Berlin, 2002
Karcher, H.: The triply periodic minimal Surfaces of Alan Schoen and their constant mean curvature companions. Manuscripta Math. 64, 291–375 (1989)
Lott, J.: Remark about heat diffusion on periodic spaces. Proceedings of the American Mathematical Society 127, 1243–1249 (1999)
Revuz, D., Yor, M.: Continuous Martingales and Brownian Motion. Grundlehren der mathematischen Wissenschaften 293, Springer Berlin, 1991
Author information
Authors and Affiliations
Corresponding author
Additional information
Mathematics Subject Classification (2000): 35B27, 60F05, 58J65
The author wants to express his gratitude toward the National Cheng Kung University in Tainan (Taiwan) for its kind hospitality.
Rights and permissions
About this article
Cite this article
Franke, B. A functional central limit theorem for diffusions on periodic submanifolds of ℝN. Probab. Theory Relat. Fields 133, 236–244 (2005). https://doi.org/10.1007/s00440-004-0425-0
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00440-004-0425-0