Bulletin of the American Mathematical Society

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Book Information:

Author: 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 pp., ISBN 0-8218-3174-7, $49.00$

1.

M. Brélot, Éléments de la théorie classique du potentiel, Les cours de Sorbonne, Centre de Documentation Universitaire, Paris V, 1959. MR 0106366

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 1242575

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 1831416

5.

J. L. Doob, Classical potential theory and its probabilistic counterpart, Springer, 1984. MR 0731258

6.

E. B. Dynkin, Markov Processes, I, II, Springer-Verlag, 1965. MR 0193671

7.

E. B. Dynkin, A probabilistic approach to one class of nonlinear differential equations, Probab. Th. Rel. Fields 89 (1991), 89-115. MR 1109476

8.

E. B. Dynkin, An introduction to branching measure-valued processes, CRM Monograph Series, vol. 6, AMS, 1994. MR 1280712

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 1371926

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 0107097

13.

I. Iscoe, On the supports of measure-valued critical branching Brownian motions, Ann. Probab. 16 (1988), 200-221. MR 0920265

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 1423232

17.

J.-F. Le Gall, Spatial branching processes, random snakes and partial differential equations, Birkhäuser, 1999. MR 1714707

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 1658392

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 1915445

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 1927455

27.

L. Véron, Singularities of Solutions of Second Order Quasilinear Equations, Pitman Research Notes in Math. 353, Addison Wesley Longman Inc., 1966. MR 1424468

28.

L. Véron, Generalized boundary value problems for nonlinear elliptic equations, Electron. J. Diff. Equ. Conf. 6, 313-342, 2001. MR 1804784

29.

S. Watanabe, A limit theorem on branching processes and continuous state branching processes, J. Math. Kyoto Univ. 8, 141-167, 2001. MR 0237008

30.

N. Wiener, Differential space, J. Math Phys. 2, 131-174, 1923.

1.

M. Brélot, Éléments de la théorie classique du potentiel, Les cours de Sorbonne, Centre de Documentation Universitaire, Paris V, 1959. MR 0106366

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 1242575

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 1831416

5.

J. L. Doob, Classical potential theory and its probabilistic counterpart, Springer, 1984. MR 0731258

6.

E. B. Dynkin, Markov Processes, I, II, Springer-Verlag, 1965. MR 0193671

7.

E. B. Dynkin, A probabilistic approach to one class of nonlinear differential equations, Probab. Th. Rel. Fields 89 (1991), 89-115. MR 1109476

8.

E. B. Dynkin, An introduction to branching measure-valued processes, CRM Monograph Series, vol. 6, AMS, 1994. MR 1280712

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 1371926

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 0107097

13.

I. Iscoe, On the supports of measure-valued critical branching Brownian motions, Ann. Probab. 16 (1988), 200-221. MR 0920265

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 1423232

17.

J.-F. Le Gall, Spatial branching processes, random snakes and partial differential equations, Birkhäuser, 1999. MR 1714707

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 1658392

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 1915445

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 1927455

27.

L. Véron, Singularities of Solutions of Second Order Quasilinear Equations, Pitman Research Notes in Math. 353, Addison Wesley Longman Inc., 1966. MR 1424468

28.

L. Véron, Generalized boundary value problems for nonlinear elliptic equations, Electron. J. Diff. Equ. Conf. 6, 313-342, 2001. MR 1804784

29.

S. Watanabe, A limit theorem on branching processes and continuous state branching processes, J. Math. Kyoto Univ. 8, 141-167, 2001. MR 0237008

30.

N. Wiener, Differential space, J. Math Phys. 2, 131-174, 1923.