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Part of the book series: Progress in Probability ((PRPR,volume 28))

Abstract

Stirring processes are related both to certain interacting particle systems and to continuous stochastic flows. Examples are given including a flow generated by Moebius automorphisms of the unit disk.

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References

  1. L. V. Ahlfors, Complex Analysis, 3d Ed., McGraw-Hill, London. 1979.

    MATH  Google Scholar 

  2. H. Aref, Stirring by chaotic advection, J. Fluid Mechanics 143 (1984), 1–21.

    Article  MathSciNet  MATH  Google Scholar 

  3. P. Baxendale, Brownian motions in the diffeomorphism group, I, Compositio Math. 53 (1984), 19–50.

    MathSciNet  MATH  Google Scholar 

  4. P. Baxendale, Asymptotic behavior of stochastic flows of diffeomorphisms: two case studies, Prob. Th. Rel. Fields 73 (1986), 51–85.

    Article  MathSciNet  MATH  Google Scholar 

  5. A. Beardon, A Primer on Riemann Surfaces, London Math. Soc. Lectures Notes 78, Cambridge 1984.

    Google Scholar 

  6. F. Bertein and A. Galvez, Une classe de systèmes de particules stables par association, Z. Wahr. Verw. Geb. 41 (1977), 73–85.

    Article  MATH  Google Scholar 

  7. J.-M. Bismut, Méchanique Aléatoire, Springer Lecture Notes in Math. 866, 1981.

    Google Scholar 

  8. A. Carverhill, Flows of stochastic dynamical systems: ergodic theory, Stochastics 14 (1985), 273–318.

    Article  MathSciNet  MATH  Google Scholar 

  9. D. Griffeath, Additive and Cancellative Interacting Particle Systems, Springer Lecture Notes in Math. 724, 1979.

    MATH  Google Scholar 

  10. T. Harris, Additive set-valued Markov processes and graphical methods, Ann. Prob. 6 (1978), 355–378.

    Article  MATH  Google Scholar 

  11. T. Harris, Brownian motions on the homeomorphisms of the plane, Ann. Prob. 9 (1981), 232–254.

    Article  MATH  Google Scholar 

  12. T. Harris, Coalescing and non-coalescing flows in R1, Stoch. Proc. Appl. 17 (1984), 187–210.

    Article  MATH  Google Scholar 

  13. E. Hille, Analytic Function Theory, Vols. I & I I, Blaisdell, NY, 1959.

    Google Scholar 

  14. T. Jaekel, Stochastic Flow with a Singular Vortex, Doctoral Dissertation, University of Southern California, 1989.

    Google Scholar 

  15. H. Kesten and G. Papanicolaou, A limit theorem for turbulent diffusion, Comm. Math. Phys. 65 (1979), 97–128.

    Article  MathSciNet  MATH  Google Scholar 

  16. H. Kunita, Lectures on Stochastic Flows and Applications,Tata Inst., Bombay, 1986 and Springer-Verlag, New York.

    MATH  Google Scholar 

  17. H. Kunita, Stochastic Flows and Stochastic Differential Equations,book in press.

    Google Scholar 

  18. W. Lee, Random Stirring of the Real Line, Ann. Prob. 2 (1974), 580–592.

    Article  MATH  Google Scholar 

  19. Y. LeJan and S. Watanabe, Stochastic flows of diffeomorphisms, Proceedings of the Taniguchi Symposium 307–332, North Holland, New York, 1984.

    Google Scholar 

  20. H. Matsumoto and I. Shigekawa, Limit theorems for stochastic flows of diffeomorphisms of jump type, Z. Wahr. Verw. Geb. 69 (1985), 507–540.

    Article  MathSciNet  MATH  Google Scholar 

  21. F. Spitzer, Interaction of Markov processes, Advances in Math. 5 (1970), 246–290.

    Article  MathSciNet  MATH  Google Scholar 

  22. J. Watkins, A central limit problem in random evolutions, Ann. Prob. 12 (1984), 480–513.

    Article  MathSciNet  MATH  Google Scholar 

  23. J. Watkins, Limit theorems for stationary random evolutions, Stoch. Proc. Applic. 19 (1985), 189–224.

    Article  MathSciNet  MATH  Google Scholar 

  24. J. Watkins, A stochastic integral representation for random evolutions, Ann. Prob. 13 (1985), 531–557.

    Article  MathSciNet  MATH  Google Scholar 

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© 1991 Springer Science+Business Media New York

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Harris, T.E. (1991). Interacting Systems, Stirrings, and Flows. In: Durrett, R., Kesten, H. (eds) Random Walks, Brownian Motion, and Interacting Particle Systems. Progress in Probability, vol 28. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0459-6_15

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  • DOI: https://doi.org/10.1007/978-1-4612-0459-6_15

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-6770-6

  • Online ISBN: 978-1-4612-0459-6

  • eBook Packages: Springer Book Archive

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