Abstract
Stochastic processes adapted to some expanding transformations are considered. It is proved that the trajectories of the resulting Markov chain stay "close" to non random orbits of transformations in question.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
M. Cranston, S. Orey, U. Rosler, Exterior Dirichlet problem and the asymptotic behavior of diffusions, in: Lecture Notes in Control and Information Sciences 25(1978), 207–220, Springer, Berlin.
H. Kesten, Some nonlinear stochastic growth models, Bull. Amer. Math. Soc. 77(1971), 492–511.
Yu. Kifer, Brownian motion and harmonic functions on manifolds of negative curvature, Theor. Prob. Appl. 2(1976), 81–95.
Yu. Kifer, General random perturbations of hyperbolic and expanding transformations, J. D'Analyse Math. 47 (1986).
M. Pinsky, Large deviations for diffusion process in: Stochastic Analysis, (1978), 271–283.
M.J.-J. Prat, Etude asymptotique du mouvement brownien sur une variété riemannienne à courbure negative, C.R. Acad. Sci. Ser. A, 272(1971), 1586–1589.
Ja.G. Sinai, Gibbs measures in ergodic theory, Russian Math. Surveys 27(1972), No. 4, 21–70.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1988 Springer-Verlag
About this paper
Cite this paper
Kifer, Y. (1988). A note on stochastic models with expanding transformations. In: Truman, A., Davies, I.M. (eds) Stochastic Mechanics and Stochastic Processes. Lecture Notes in Mathematics, vol 1325. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0077922
Download citation
DOI: https://doi.org/10.1007/BFb0077922
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-50015-5
Online ISBN: 978-3-540-45887-6
eBook Packages: Springer Book Archive