|
Book Review
The AMS does not provide abstracts of book reviews.
You may download the entire review from the links below.
Retrieve article in:
PDF
Book Information
Author(s):
E. B. Dynkin
Title:
Diffusions, superdiffusions and partial differential equations
Additional book information:
Colloquium Publications, vol. 50, American Mathematical Society,
Providence, RI,
2002,
xi + 236,
$49.00,
ISBN 0-8218-3174-7
References:
-
- 1.
- M. Brélot, Éléments de la théorie classique du potentiel, Les cours de Sorbonne, Centre de Documentation Universitaire, Paris V, 1959. MR 21:5099
- 2.
- R. K. Courant, K. Friedrichs and H. Lewy, Über die partiellen Differenzengleichungen der mathematischen Physik. Math. Ann. 100 (1928), 32-74.
- 3.
- D. A. Dawson, Measure-valued Markov processes, in École d'Été de Probabilités de Saint Flour XXI, Lecture Notes in Mathematics 1541, Springer-Verlag, 1993, 1-261. MR 94m:60101
- 4.
- D. A. Dawson and K. Fleischmann, Catalytic and mutually catalytic branching, in Infinite Dimensional Stochastic Analysis, eds. Ph. Clément, F. den Hollander, J. van Neerven and B. de Pagter, Royal Netherlands Academy, Amsterdam, 145-170, 2000. MR 2002f:60164
- 5.
- J. L. Doob, Classical potential theory and its probabilistic counterpart, Springer, 1984. MR 85k:31001
- 6.
- E. B. Dynkin, Markov Processes, I, II, Springer-Verlag, 1965. MR 33:1887
- 7.
- E. B. Dynkin, A probabilistic approach to one class of nonlinear differential equations, Probab. Th. Rel. Fields 89 (1991), 89-115. MR 92d:35090
- 8.
- E. B. Dynkin, An introduction to branching measure-valued processes, CRM Monograph Series, vol. 6, AMS, 1994. MR 96f:60145
- 9.
- E. B. Dynkin, A new inequality for superdiffusions and its applications to nonlinear differential equations, manuscript, 2003.
- 10.
- E. B. Dynkin, Superdiffusions and positive solutions of nonlinear partial differential equations, to appear in Uspekhi Mat. Nauk., 2003.
- 11.
- E. B. Dynkin and S. E. Kuznetsov, Superdiffusions and removable singularities for quasilinear partial differential equations, Comm. Pure Appl. Math. 49 (1996), 125-176. MR 97m:60114
- 12.
- G. Hunt, Markov processes and potentials I, II, III, Illinois J. Math. 1 (1957), 44-93; 1 (1957), 316-369; 2 (1958), 151-213. MR 19:951g, MR 21:5824
- 13.
- I. Iscoe, On the supports of measure-valued critical branching Brownian motions, Ann. Probab. 16 (1988), 200-221. MR 88j:60097
- 14.
- S. Kakutani, Two dimensional Brownian moion and harmonic functions, Proc. Imp. Acad. Tokyo 20 (1944), 227-233. MR 7:315b
- 15.
- S. Kakutani, Markov processes and the Dirichlet problem, Proc. Imp. Acad. Tokyo 21, 227-233, 1945. MR 11:357h
- 16.
- J.-F. Le Gall, A probabilistic Poisson representation for positive solutions
in a planar domain, Comm. Pure Appl. Math. 50 (1997), 69-103. MR 98c:60144 - 17.
- J.-F. Le Gall, Spatial branching processes, random snakes and partial differential equations, Birkhäuser, 1999. MR 2001g:60211
- 18.
- J.-F. Le Gall and L. Mytnik, Regularity and irregularity of the exit measure density for
stable super-Brownian motion, 2003 preprint. - 19.
- R. S. Martin, Minimal positive harmonic functions, Trans. Amer. Math. Soc. 49 (1941), 137-172. MR 2:292h
- 20.
- M. B. Mselati, Classification et répresentation probabiliste des solutions positives de
dans un domaine, Thèse Doctorat de l'Université Paris 6, 2002. - 21.
- M. B. Mselati, Classification et répresentation probabiliste des solutions positives d'une équation elliptique semi-linéaire, C. R. Acad. Sci. Paris Ser. I 335, 733-738, 2002.
- 22.
- M. Marcus and L. Véron, The boundary trace of positive solutions of semilinear elliptic equations, I. The subcritical case, Arch. Rat. Mech. Anal. 144 (1998), 201-231. MR 2000a:35077
- 23.
- M. Marcus and L. Véron, Capacitary estimates of solutions of a class of nonlinear elliptic equations, C. R. Acad. Sci. Paris Ser. I 336, 2003.
- 24.
- E. A. Perkins, Dawson-Watanabe Superprocesses and Measure-valued Diffusions, Ecole d'été de probabilités (Saint Flour, 1999), Lecture Notes in Math. 1781, Springer, 2002, 125-324. MR 2003k:60104
- 25.
- H. B. Phillips and N. Wiener, Nets and Dirichlet problem, J. Math. Phys. 2, 105-124, 1923.
- 26.
- G. Slade, Scaling limits and super-Brownian motion, Notices AMS, 49, 1056-1067, 2002. MR 2003g:60170
- 27.
- L. Véron, Singularities of Solutions of Second Order Quasilinear Equations, Pitman Research Notes in Math. 353, Addison Wesley Longman Inc., 1966. MR 98b:35053
- 28.
- L. Véron, Generalized boundary value problems for nonlinear elliptic equations, Electron. J. Diff. Equ. Conf. 6, 313-342, 2001. MR 2001j:35099
- 29.
- S. Watanabe, A limit theorem on branching processes and continuous state branching processes, J. Math. Kyoto Univ. 8, 141-167, 2001. MR 38:5301
- 30.
- N. Wiener, Differential space, J. Math Phys. 2, 131-174, 1923.
Additional Information:
Reviewer(s):
Donald
Dawson
Affiliation:
Carleton University and McGill University
Email:
ddawson@math.carleton.ca
Review Information:
Journal:
Bull. Amer. Math. Soc.
41
(2004),
245-252.
MSC
(2000):
Primary 60J60, 35-XX;
Secondary 35K55, 60J65
PII:
S 0273-0979(04)01002-X
Posted:
January 8, 2004
Copyright of article:
Copyright
2004,
American Mathematical Society
|