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References
Barlow, Martin T.; Evans, Steven N.; Perkins, Edwin A. Collision local times and measure-valued processes.
Canad. J. Math. 43 (1991), no. 5, 897--938. MR1138572 (93a:60119) |
Bass, Richard F.; Perkins, Edwin A. Countable systems of degenerate stochastic differential equations with applications to super-Markov chains.
Electron. J. Probab. 9 (2004), no. 22, 634--673 (electronic). MR2110015 (2005j:60113) |
Bramson, M.; Durrett, R.; Swindle, G.. Statistical mechanics of crabgrass.
Ann. Probab. 17 (1989), no. 2, 444--481. MR0985373 (90b:60134) |
J. Cox, R. Durrett, and E. Perkins,
Rescaled Particle Systems Converging to Super-Brownian
Motion.
In M. Bramson and R. Durrett, editors, Perplexing Problems
in Probability. Festschrift in Honor of Harry Kesten, pages
269--284, Birkhäuser Boston, 1999.
MR1703136 (2001d:60104) |
Cox, J. Theodore; Durrett, Richard; Perkins, Edwin A. Rescaled voter models converge to super-Brownian motion.
Ann. Probab. 28 (2000), no. 1, 185--234. MR1756003 (2001d:60105) |
Dawson, D. A. Geostochastic calculus.
Canad. J. Statist. 6 (1978), no. 2, 143--168. MR0532855 (81g:60076) |
Dawson, Donald A.; Etheridge, Alison M.; Fleischmann, Klaus; Mytnik, Leonid; Perkins, Edwin A.; Xiong, Jie. Mutually catalytic branching in the plane: finite measure states.
Ann. Probab. 30 (2002), no. 4, 1681--1762. MR1944004 (2003k:60252) |
Dawson, Donald A.; Perkins, Edwin A. Long-time behavior and coexistence in a mutually catalytic branching model.
Ann. Probab. 26 (1998), no. 3, 1088--1138. MR1634416 (99f:60167) |
Donnelly, Peter; Kurtz, Thomas G. Particle representations for measure-valued population models.
Ann. Probab. 27 (1999), no. 1, 166--205. MR1681126 (2000f:60108) |
Durrett, R. Predator-prey systems.
Asymptotic problems in probability theory: stochastic models and diffusions on fractals (Sanda/Kyoto, 1990),
37--58, Pitman Res. Notes Math. Ser., 283, Longman Sci. Tech., Harlow, 1993. MR1354150 (96k:60255) |
R. Durrett and S. Levin.
Allelopathy in spatially distributed populations.
J. Theor. Biol. 185:165--172, 1997.
|
Durrett, Richard; Perkins, Edwin A. Rescaled contact processes converge to super-Brownian motion in two or more dimensions.
Probab. Theory Related Fields 114 (1999), no. 3, 309--399. MR1705115 (2000f:60149) |
Durrett, Richard. Probability: theory and examples.
Second edition.
Duxbury Press, Belmont, CA, 1996. xiii+503 pp. ISBN: 0-534-24318-5 MR1609153 (98m:60001) |
Dynkin, Eugene B. An introduction to branching measure-valued processes.
CRM Monograph Series, 6. American Mathematical Society, Providence, RI, 1994. x+134 pp. ISBN: 0-8218-0269-0 MR1280712 (96f:60145) |
Ethier, Stewart N.; Kurtz, Thomas G. Markov processes.
Characterization and convergence.
Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics. John Wiley & Sons, Inc., New York, 1986. x+534 pp. ISBN: 0-471-08186-8 MR0838085 (88a:60130) |
Evans, Steven N.; Perkins, Edwin A. Measure-valued branching diffusions with singular interactions.
Canad. J. Math. 46 (1994), no. 1, 120--168. MR1260341 (94j:60099) |
Evans, Steven N.; Perkins, Edwin A. Collision local times, historical stochastic calculus, and competing superprocesses.
Electron. J. Probab. 3 (1998), No. 5, 120 pp. (electronic). MR1615329 (99h:60098) |
Fleischmann, Klaus; Mytnik, Leonid. Competing species superprocesses with infinite variance.
Electron. J. Probab. 8 (2003), no. 8, 59 pp. (electronic). MR1986840 (2004f:60204) |
Harris, Theodore E. The theory of branching processes.
Die Grundlehren der Mathematischen Wissenschaften, Bd. 119 Springer-Verlag, Berlin; Prentice-Hall, Inc., Englewood Cliffs, N.J. 1963 xiv+230 pp. MR0163361 (29 #664) |
Ikeda, Nobuyuki; Watanabe, Shinzo. Stochastic differential equations and diffusion processes.
North-Holland Mathematical Library, 24. North-Holland Publishing Co., Amsterdam-New York; Kodansha, Ltd., Tokyo, 1981. xiv+464 pp. ISBN: 0-444-86172-6 MR0637061 (84b:60080) |
Jacod, Jean; Shiryaev, Albert N. Limit theorems for stochastic processes.
Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 288. Springer-Verlag, Berlin, 1987. xviii+601 pp. ISBN: 3-540-17882-1 MR0959133 (89k:60044) |
Kuznetsov, S. E. Regularity properties of a supercritical superprocess.
The Dynkin Festschrift,
221--235, Progr. Probab., 34, Birkhäuser Boston, Boston, MA, 1994. MR1311722 (96m:60168) |
Liggett, Thomas M. Interacting particle systems.
Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 276. Springer-Verlag, New York, 1985. xv+488 pp. ISBN: 0-387-96069-4 MR0776231 (86e:60089) |
C. Mueller and R. Tribe,
Stochastic pde's arising from the long range contact and long range
voter processes.
Probabability Theory and Related Fields,
102 (1995), 519-546.
MR1346264 (96k:60259)
|
Mytnik, Leonid. Uniqueness for a competing species model.
Canad. J. Math. 51 (1999), no. 2, 372--448. MR1697149 (2000g:60112) |
Perkins, Edwin. Dawson-Watanabe superprocesses and measure-valued diffusions.
Lectures on probability theory and statistics (Saint-Flour, 1999),
125--324, Lecture Notes in Math., 1781, Springer, Berlin, 2002. MR1915445 (2003k:60104) |
Walsh, John B. An introduction to stochastic partial differential equations.
École d'été de probabilités de Saint-Flour, XIV---1984,
265--439, Lecture Notes in Math., 1180, Springer, Berlin, 1986. MR0876085 (88a:60114) |