# 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: Primary 60H99; Secondary 58D25, 60B05, 60G99, 60J25

### 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