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Constructing nonhomeomorphic stochastic flows


About this Title

R. W. R. Darling

Publication: Memoirs of the American Mathematical Society
Publication Year 1987: Volume 70, Number 376
ISBNs: 978-0-8218-2439-9 (print); 978-1-4704-0796-4 (online)
DOI: http://dx.doi.org/10.1090/memo/0376
MathSciNet review: 912641
MSC (1991): Primary 60H99; Secondary 58D25, 60B05, 60G99, 60J25

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Table of Contents


Chapters

  • Part I. Introduction
  • 1. Background
  • 2. Outline of the main results
  • 3. Pure stochastic flows
  • Part II. Construction of a pure stochastic flow with given finite-dimensional distributions
  • 4. Convolution of measures with respect to composition of functions
  • 5. A projective system for building a pure stochastic flow
  • 6. Existence theorem for pure stochastic flows
  • Part III. Construction of a stochastic flow assuming almost no fixed points of discontinuity
  • 7. Probability measures with almost no fixed points of discontinuity
  • 8. Fluid Radon probability measures and their convolution
  • 9. Existence theorem for pure stochastic flows assuming almost no fixed points of discontinuity
  • Part IV.
  • 10. Construction of a convolution semigroup of probability measures from finite dimensional Markov processes
  • Part V. Covariance functions and the corresponding sets of finite-dimensional motions
  • 11. Algebraic properties of the covariance function
  • 12. Constructing the finite-dimensional motions
  • 13. Stochastic continuity in the non-isotropic case
  • 14. Stochastic continuity and coalescence in the isotropic case
  • 15. The one-dimensional case
  • 16. An example in dimension two (due to T. E. Harris)
  • Part VI. The geometry of coalescence
  • 17. Coalescence times and the coalescent set process
  • Appendix A. Baire sets, Borel sets, and Radon probability measures
  • Appendix B. Projective systems of probability spaces