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A note on stochastic models with expanding transformations

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Stochastic Mechanics and Stochastic Processes

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1325))

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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.

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References

  1. 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.

    Google Scholar 

  2. H. Kesten, Some nonlinear stochastic growth models, Bull. Amer. Math. Soc. 77(1971), 492–511.

    Article  MathSciNet  MATH  Google Scholar 

  3. Yu. Kifer, Brownian motion and harmonic functions on manifolds of negative curvature, Theor. Prob. Appl. 2(1976), 81–95.

    Article  MathSciNet  MATH  Google Scholar 

  4. Yu. Kifer, General random perturbations of hyperbolic and expanding transformations, J. D'Analyse Math. 47 (1986).

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  5. M. Pinsky, Large deviations for diffusion process in: Stochastic Analysis, (1978), 271–283.

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  6. 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.

    MathSciNet  MATH  Google Scholar 

  7. Ja.G. Sinai, Gibbs measures in ergodic theory, Russian Math. Surveys 27(1972), No. 4, 21–70.

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Aubrey Truman Ian M. Davies

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© 1988 Springer-Verlag

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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

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  • DOI: https://doi.org/10.1007/BFb0077922

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50015-5

  • Online ISBN: 978-3-540-45887-6

  • eBook Packages: Springer Book Archive

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