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Birth and Death on a Flow

  • Erhan Çinlar
  • John S. Kao
Part of the Progress in Probability book series (PRPR, volume 27)

Abstract

In recent years there has been much interest in the equilibrium behavior of stochastic flows; see for instance Baxendale [1], Carverhill [2], Le Jan [6], [7] and [8]. Most of the work seems to be concentrated on the limiting distribution, as t → ∞, of the random measure
$${\mu _t}(\omega ,A) = {\mu _0}\{ x:F_{0,t}^\omega x \in A\} $$
for a stochastic flow F = {F s,t : 0 ≤ st ≤ ∞} and a given mass distribution μ0 with total mass 1. In some applications, notably in transport of pollutant particles by groundwater flows, one is interested in similar questions but with creation and annihilation of mass over time and space.

Keywords

Random Measure Birth Process Poisson Random Measure Stochastic Flow Transition Semigroup 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    P. Baxendale. Asymptotic behavior of stochastic flows of diffeomorphisms: two case studies. Prob. Theory Rel. Fields 73 (1986), 51–85.MathSciNetMATHCrossRefGoogle Scholar
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    A. P. Carverhill. Flows of stochastic dynamical systems: ergodic theory. Stochastics 14 (1985), 209–226.MathSciNetMATHCrossRefGoogle Scholar
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    E. Çinlar. Introduction to Stochastic Processes. Prentice-Hall, Englewood Cliffs, 1975.MATHGoogle Scholar
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    O. Kallenberg. Random Measures. Academie-Verlag, Berlin, 1983.MATHGoogle Scholar
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    H. Kunita. Lectures on Stochastic Flows and Applications. Tata Institute of Fundamental Research. Springer-Verlag, Berlin, 1986.MATHGoogle Scholar
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    Y. Le Jan. Flots de diffusion dans ℝd. C. R. Acad. Sci. Paris Ser. I 294 (1982), 697–699.MATHGoogle Scholar
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    —. Equilibre et exposants de Lyapunov de certaines flots Browniens. C. R. Acad. Sci. Paris Ser. I 298 (1984), 361–364.MATHGoogle Scholar
  8. [8]
    —. Equilibrium state for a turbulent flow of diffusion. Research Notes in Math. 124, 83–93. Pitman, Boston, 1985.Google Scholar

Copyright information

© Springer Science+Business Media New York 1992

Authors and Affiliations

  • Erhan Çinlar
    • 1
  • John S. Kao
    • 1
  1. 1.Princeton UniversityUSA

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