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Book Review

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Book Information:

Authors: L. C. G. Rogers and D. Williams
Title: Diffusions, Markov processes, and martingales, Volume One: Foundations, Second Edition
Additional book information: John Wiley & Sons, Chichester, West Sussex, England, 1994, xx + 386 pp., ISBN 0-471-95061-0, $79.95

References [Enhancements On Off] (What's this?)

  • 1. Désiré André, Solution directe du problème résolu par M. Bertrand, C. R. Acad. Sci. Paris 105 (1887), 436-437.
  • 2. Kai Lai Chung, Probabilistic approach to the equilibrium problem, Ann. Inst. Fourier Grenoble 23 (1973), 313-322. MR 52:12098
  • 3. -, Lectures from Markov Processes to Brownian Motion, Springer-Verlag, 1982. MR 84c:60091
  • 4. J. L. Doob, Semimartingales and subharmonic functions, Trans. Amer. Math. Soc. 77 (1954), 86-121. MR 16:269a
  • 5. -, Classical Potential Theory and its Probabilistic Counterpart, Springer-Verlag, 1984. MR 85k:31001
  • 6. D. A. Dawson, Measure-valued Markov processes, pp. 1-260 in Ecole d'Eté de Probabilités de Saint-Flour XXI - 1991 (editor: P. L. Hennequin), Lecture Notes in Mathematics, vol. 1541, Springer-Verlag, 1993. MR 94m:60101
  • 7. Eugene B. Dynkin, An Introduction to Branching Measure-Valued Processes, American Mathematical Society, 1994. MR 96f:60145
  • 8. Neil Falkner and P. J. Fitzsimmons, Stopping distributions for right processes, Probab. Th. Rel. Fields 89 (1991), 301-318. MR 92j:60091
  • 9. M. Fukushima, Y. Oshima, and M. Takeda, Dirichlet forms & symmetric Markov Processes, Walter de Gruyter, 1994. MR 96f:60126
  • 10. R. K. Getoor, Excessive Measures, Birkhäuser, 1990. MR 92i:60135
  • 11. R. K. Getoor and M. J. Sharpe, Last exit times and additive functionals, Ann. Probab. 1 (1973), 550-569. MR 50:5951
  • 12. G. A. Hunt, Markov processes and potentials I, Illinois J. Math. 1 (1957), 44-93. MR 19:951g
  • 13. -, Markov processes and potentials II, Illinois J. Math. 1 (1957), 316-369. MR 19:951g
  • 14. -, Markov processes and potentials III, Illinois J. Math. 2 (1958), 151-213. MR 21:5824
  • 15. Shizuo Kakutani, Two dimensional Brownian motion and harmonic functions, Proc. Imp. Acad. Tokyo 20 (1944), 707-714. MR 7:315b
  • 16. -, Markov processes and the Dirichlet problem, Proc. Japan Acad. 21 (1945), 227-233. MR 11:357h
  • 17. Frank Knight, Note on regularization of Markov processes, Illinois J. Math. 9 (1965), 548-552. MR 31:1713
  • 18. Paul Lévy, Théorie de l'Addition des Variables Aléatoires, Gauthier-Villars, Paris, 1937.
  • 19. Michel Loève, Probability Theory, Third Edition, Van Nostrand, 1963. MR 34:3596
  • 20. -, Paul Lévy, 1886-1971, Ann. Probab. 1 (1973), 1-18. MR 49:7083
  • 21. Zhi-Ming Ma and Michael Rockner, Introduction to the theory of (non-symmetric) Dirichlet forms, Springer-Verlag, 1992. MR 94d:60119
  • 22. H. P. McKean, A probabilistic interpretation of equilibrium charge distributions, J. Math. Kyoto Univ. 4 (1965), 617-625. MR 32:3130
  • 23. Daniel Ray, Resolvents, transition functions, and strongly Markovian processes, Ann. Math. 70 (1959), 43-72. MR 21:6027
  • 24. T. Ueno, On recurrent Markov processes, Kôdai Math. Sem. Rep. 12 (1960), 109-142. MR 22:10017

Review Information:

Reviewer: Neil Falkner
Affiliation: Ohio State University
Email: falkner@math.ohio-state.edu
Journal: Bull. Amer. Math. Soc. 34 (1997), 57-62
MSC (1991): Primary 60Jxx; Secondary 60G15, 60G42, 60G44
DOI: https://doi.org/10.1090/S0273-0979-97-00693-9
Review copyright: © Copyright 1997 American Mathematical Society
American Mathematical Society