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Book Review
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Book Information
Author(s):
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.,
$79.95,
ISBN 0-471-95061-0
References:
- 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
Additional Information:
Reviewer(s):
Neil
Falkner
Affiliation:
Ohio State University
Email:
falkner@math.ohio-state.edu
Review Information:
Journal:
Bull. Amer. Math. Soc.
34
(1997),
57-62.
MSC
(1991):
Primary 60Jxx;
Secondary 60G15, 60G42, 60G44
DOI:
10.1090/S0273-0979-97-00693-9
PII:
S 0273-0979(97)00693-9
Copyright of article:
Copyright
1997,
American Mathematical Society
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