Publications

Publications

[96] Remco van der Hofstad, Mark Holmes and Edwin A. Perkins Criteria for convergence
to super-Brownian motion on path space
, 68 pages, submitted, 2014.

[95] Ted Cox and Edwin A. Perkins A complete convergence theorem
for voter model perturbations
, 52 pages, to appear in Ann. Appl. Prob. (2013).

[94] Carl Mueller, Leonid Mytnik, and Edwin A. Perkins Nonuniqueness for a parabolic SPDE with 3/4-epsilon diffusion coefficients , 74 pages, to appear in Ann. Prob. (2013).

[93] Steven P. Lalley, Edwin A. Perkins, and Xinghua Zheng A phase transition for measure-valued SIR epidemic processes , 68 pages, to appear in Ann. Prob. (2013).

[92] Richard Durrett, Ted Cox and Edwin Perkins, Voter model perturbations and
reaction diffusion equations
, Asterisque 349, 113 pp, 2013.

[91] Richard Bass and Edwin Perkins, On uniqueness in law for parabolic SPDE's
and infinite dimensional SDE's
, Elect. J. Prob. 17, 54 pages (2012).

[90] Chris Burdzy, Carl Mueller and Edwin Perkins,
Non-uniqueness for non-negative solutions of parabolic SPDE's
, 28 pages,
to appear in Burkholder volume of the Ill.J. Math (2011).

[89] Ted Cox, Mathieu Merle and Edwin Perkins,
Co-existence in a two-dimensional Lotka-Volterra model
,
Elect. J. Probability 15, 1190--1266 (2010).

[88] Leonid Mytnik and Edwin Perkins, Pathwise uniqueness for stochastic heat equations
with Holder continuous coefficients: the white noise case
,
Prob. Th. Rel. Fields 149, pp. 1--96 (2011).

[87] Richard Bass and Edwin Perkins, A new technique for proving
uniqueness for martingale problems
, 9 pages,
to appear in Tribute to Jean-Michel Bismut,
Eds. R. Leandre, X. Ma, W. Zhang, Asterisque (2009).

[86] Richard Bass and Edwin Perkins, Degenerate stochastic differential
equations arising from catalytic branching networks
,
Elect. J. Probability 13, 1808-1885 (2008).

[85] Ted Cox and Edwin Perkins, Renormalization of the two-dimensional
Lotka-Volterra Model,
Ann. of Applied Probability 18, 747-812 (2008).

[84] Mark Holmes and Edwin Perkins, Weak convergence of measure-valued
processes and r-point functions,
Ann. Probability 35, 1769-1782 (2007).

[83] Ted Cox and Edwin Perkins, Survival and coexistence in
stochastic spatial Lotka-Volterra models
,
Prob. Theory and Rel. Fields 139, 89-142 (2007).

[82] Donald Dawson and Edwin Perkins, On the uniqueness problem for
catalytic branching networks and other singular diffusions
,
Illinois J. Math 50, 323-383 (2006).

[81] Leonid Mytnik, Edwin Perkins and Anja Sturm, On pathwise uniqueness for
stochastic heat equations with non-Lipschitz coefficients
, Ann.
Probability 34, 1910-1959 (2006).

[80] Siva Athreya, Richard Bass, Maria Gordina and Ed Perkins,
Infinite-dimensional sde's of Ornstein-Uhlenbeck type, Stoch.
Proc. Appl. 116, 381-406 (2006).

[79] Richard Durrett, Leonid Mytnik and Ed Perkins, Competing
super-Brownian motions as limits of interacting particle systems
,
Elect. J. Probability 10, 1147-1220 (2005).

[78] Richard Bass and Edwin Perkins, Countable systems of degenerate
stochastic differential equations with applications to super-Markov
chains
, Elect. J. Prob. 9, 634-673 (2004).

[77] Ted Cox and Ed Perkins, Rescaled Lotka-Volterra models converge to
super-Brownian motion
, Ann. Prob. 33, 904-947 (2005).

[76] Siva Athreya, Richard Bass and Edwin Perkins, Holder norm
estimates for elliptic operators on finite and infinite dimensional
spaces
, Trans. Amer. Math. Soc. 357, 5001-5029 (2005).

[75] Ted Cox and Ed Perkins, An application of the voter
model-super-Brownian motion invariance principle
, Ann. Inst.
Henri Poincare' 40, 25-32 (2004).

[74] Ed Perkins, Super-Brownian motion and criticial spatial stochastic systems,
Bull. Can. Math. Soc. 47, 280--297 (2004).

[73] Leonid Mytnik and Ed Perkins, Regularity and irregularity of
densities for stable branching superprocesses,
Ann. Prob. 31, 1413--1440 (2003).

[72] Richard Bass and Edwin Perkins, Degenerate stochastic differential
equations and weighted Holder spaces, Trans. Amer. Math. Soc. 355, 373--405
(2002).

[71] Don Dawson, Alison Etheridge, Klaus Fleischmann, Leonid Mytnik, Ed
Perkins and Jie Xiong, Mutually catalytic super-Brownian motion in the
plane, Ann. Prob. 30, 1681--1762 (2002).

[70] Don Dawson, Alison Etheridge, Klaus Fleischmann, Leonid Mytnik, Ed
Perkins and Jie Xiong, Mutually catalytic branching in the plane:
infinite measure states, Elect. J. Probability 7 (64 pages) (2002).

[69] Siva Athreya, Martin Barlow, Richard Bass, Ed Perkins, Degenerate
Stochastic differential equations and super-Markov chains,
Prob. Theory Rel. Fields 123, 484--520 (2002).

[68] Don Dawson, Klaus Fleischmann, Leonid Mytnik, Ed Perkins and Jie
Xiong, Mutually catalytic super-Brownian branching in the plane:
uniqueness Ann. Inst. Henri Poincar\'e Prob. et Stat. 39,
135-191 (2003).

[67] Richard Bass and Edwin Perkins, On the martingale problem for
Super-Brownian motion, Seminaire de Probabilite's XXXV, 195-201 (2001)

[66] Ted Cox, Achim Klenke and Edwin Perkins, Weak convergence and
linear systems duality, Proceedings of the International Conference on
Stochastic Models, 1998, CMS Conference Proceedings, 26, 41-66 (2000).

[65] Carl Mueller and Edwin Perkins, Extinction for two parabolic PDE's
on the lattice, Ann. Inst. Henri Poincare. Prob. et Stat. 36, 301-338 (2000).

[64] Ted Cox, Richard Durrett and Edwin Perkins, Rescaled Voter Models
Converge to Super-Brownian Motion, Ann. Prob., 28, 185-234 (2000).

[63] Ted Cox, Richard Durrett and Edwin Perkins, Rescaled Particle
Systems Converging to Super-Brownian Motion, pp. 269-284, Perplexing
Problems in Probability--Festschrift in Honor of Harry Kesten (1999).

[62] Donald Dawson and Edwin Perkins, Measure-valued processes
and renormalizaton of branching particle systems pp 45-106 Stochastic
pde's:Six Perspectives, AMS Math. Surveys and Monographs (1999).

[61] Donald Dawson and Edwin Perkins, Long-time Behaviour and
co-existence in a mutually catalytic branching model (49 pages),
Annals Prob. 26, 1088-1138 (1998).

[60] Steven Evans and Edwin Perkins, Collision local times, historical
stochastic calculus and competing superprocesses (125 pages), Elect. J.
Prob., March, 1998.

[59] Richard Durrett and Edwin Perkins, Rescaled Contact Processes
Converge to Super-Brownian Motion for d greater than or equal to 2,
Prob. Theory and Related Fields 114, 309-399 (1999).

[58] Edwin A. Perkins and S. James Taylor, The multifractal
spectrum of super-Brownian motion, Annales d'Institut Henri Poincare 34,
97-138 (1998).

[57] Donald Dawson and Edwin Perkins, Measure-valued processes
and renormalizaton of branching particle systems (to appear in
Stochastic pde's:Six Perspectives, AMS Math. Surveys and Monographs) (63 pages)
(1997).

[56] Hassan Allouba, Richard Durrett, John Hawkes and Edwin Perkins,
Super-tree random measures, J. Theoretical Probability 10, 773-794 (1997).

[55] Martin Barlow, Robin Pemantle and Edwin Perkins, DLA on
a binary tree, Prob. Theory and Rel. Fields 107, 1-60 (1997).

[54] Donald Dawson and Edwin Perkins, Measure-valued processes and
stochastic partial differential equations, Can. J. Math., Volume of Invited
papers for 50th Anniversary of the CMS, 19-60 (1996).

[53] Edwin Perkins, On the martingale problem for interactive
measure-valued branching diffusions, Memoirs of the American Math. Soc. 115,
No. 549, 1-89 (1995).

[52] J.F. Le Gall and Edwin Perkins, The exact Hausdorff measure of
two-dimensional super-Brownian motion, Annals of Prob. 23,1719-1747 (1995).

[51] J.F. Le Gall, Edwin Perkins and S.J. Taylor, The packing
measure of super-Brownian motion, Stoch. Proc. Appl. 59, 1-20 (1995).

[50] Steven N. Evans and Edwin Perkins, Explicit stochastic integral
representations for superprocesses, Annals of Prob. 23, 1772-1815 (1995).

[49] Steve Evans and Edwin Perkins, Measure-valued branching diffusions
with singular interactions, Can. J. Math. 46, 120-168 (1994).

[48] Martin Barlow and Edwin Perkins, On the filtration of historical Brownian
motion, Annals of Prob. 22, 1273-1294 (1994).

[47] Edwin Perkins, On the strong Markov property of the support of
super-Brownian motion, in The Dynkin Festschrift, M. Freidlin (ed.) 307-326
(1994).

[46] Edwin Perkins, Measure-valued diffusions and interactions, Proceedings of
the I.C.M., Zurich,1036-1046 (1995).

[45] Carl Mueller and Edwin Perkins, The compact support property for
solutions to the heat equation with noise, Prob. Theory and Related Fields
93, 325-358 (1992).

[44] Edwin Perkins, Measure-valued branching diffusions with spatial
interactions, Prob. Theory and Related Fields 94, 189-245 (1992).

[43] Edwin Perkins, Conditional Dawson-Watanabe processes and Fleming-Viot
processes,
Seminar on Stochastic Processes 1991, 143-156, Ed. E. Cinlar,
K.L. Chung R.K. Getoor (1991).

[42] Don Dawson and Edwin Perkins, Historical processes. Memoirs of the
Amer. Math. Soc., 93, no. 454, 179 pages (1991).

[41] Martin Barlow, Steven Evans and Edwin Perkins, Collision local times
and measure-valued processes, Can. J. Math. 43, 897-938 (1991).

[40] On the continuity of measure-valued processes, Seminar on Stochastic
Processes 1990, E. Cinlar, P.J. Fitzsimmons and R.J. Williams (eds.)
261-268 (1991).

[39] Steve Evans and Edwin Perkins, An absolute continuity result for
measure-valued diffusions and applications, Trans. Amer. Math. Soc. 325,
661-682 (1991).

[38] Steven Evans and Edwin Perkins, Measure-valued Markov branching
processes conditioned on non-extinction, Israel J. Math 71, 329-337 (1990).

[37] Edwin Perkins, Polar sets and multiple points for super-Brownian
motion, Ann. Probability 18 453-491 (1990).

[36] Martin Barlow and Edwin Perkins, On pathwise uniqueness and expansion
of filtrations.  Seminaire de Probabilities XXIV, J. Azema, P.A. Meyer, M.
Yor (eds.), 194-209 (1990).

[35] Martin Barlow and Edwin Perkins, Symmetric Markov chains in Zd: How
fast can they move?  Prob. Theory and Related Fields 82, 95-108 (1989).

[34] Donald Dawson, Ian Iscoe and Edwin Perkins, Super-Brownian motion:
path properties and hitting probabilities.  Prob. Theory and Related Fields
83, 135-206 (1989).

[33] Martin Barlow and Edwin Perkins, Sample path properties of stochastic
integrals and stochastic differentiation, Stochastics 27, 261-293 (1989).

[32] Edwin Perkins, The exact Hausdorff measure of the closed support of
super-Brownian motion.  Annales de l'Institut Henri Poincare, 25, 205-224
(1989).

[31] Edwin Perkins and S. James Taylor, Measuring close approaches on a
Brownian path, Annals of Probability 16, 1458-1480 (1988).

[30] Edwin Perkins, A space-time property of a class of measure-valued
diffusions, Trans. Amer. Math. Soc. 305, 743-796 (1988).

[29] Martin Barlow and Edwin Perkins, Brownian motion on the Sierpinski
gasket, Prob. Theory and Related Fields, 79, 543-623 (1988).

[28] Edwin Perkins and S. James Taylor, Uniform Hausdorff measure results
for stable processes, Probability Theory and Related Fields (formerly
Z.F.W.) 76, 257-289 (1987).

[27] Martin Barlow, Edwin Perkins, S. James Taylor, Two uniform intrinsic
constructions for the local time of a class of Levy processes, Ill. J.
Math., 30, 19-65 (1986).

[26] Martin Barlow and Edwin Perkins, The behaviour of Brownian motion at a
slow point, Trans. Amer. Math. Soc., 296, 741-775 (1986).

[25] Martin Barlow, Edwin Perkins, S. James Taylor, The behaviour and
construction of local times for Levy processes, Seminar on Stochastic
Processes, 1984, 23-54, ed. E. Cinlar, Birkhauser (1986).

[24] Edwin Perkins, On the continuity of the local time of stable processes,
Seminar on Stochastic Processes, 1984, 151-164, ed. E. Cinlar, Birkhauser
(1986).

[23] Edwin Perkins, The Cereteli-Davis H1-embedding theorem and an optimal
embedding in Brownian motion
,
Seminar on Stochastic Processes 1985, 172-223, Ed. E. Cinlar,
K.L. Chung R.K. Getoor (1986).

[22] Edwin Perkins, Multiple Stochastic Integrals - A Counter-example,
Seminaire de Probabilities XIX, Lect. Notes in Math 1123, Springer 258-262
(1985).

[21] Burgess Davis and Edwin Perkins, On Brownian slow points - the
critical cases, Annals of Probability 13, 774-803 (1985).

[20] Martin Barlow and Edwin Perkins, Levels at which every Brownian
excursion is exceptional, Seminaire de Probabilities XVIII, Lect. Notes in
Math 1059 Springer  1-28 (1984).

[19] Martin Barlow and Edwin Perkins, One dimensional stochastic
differential equations involving a singular increasing process, Stochastics
Vol. 12 229-249 (1984).

[18] Priscilla Greenwood and Edwin Perkins, Limit theorems for excursions
from a moving boundary, Theory of Probability and its Applications 29
517-528 (1984).

[17] Edwin Perkins, Stochastic integrals and progressive measurability - an
example, Seminaire de Probabilites XVII, Lect. Notes in Math. 986,
Springer, 67-71 (1983).

[16] Edwin Perkins, Stochastic processes and nonstandard analysis, Vol. 983,
Springer, 162-185 (1983).

[15] Martin Barlow and Edwin Perkins, Strong Existence, Uniqueness and
Non-uniqueness in an equation involving local time, Seminaire de
Probabilites XVII, Lect. Notes in Math. 986, Springer, 32-61 (1983).

[14] Douglas Hoover and Edwin Perkins, Nonstandard construction of the
stochastic integral and applications to stochastic differential equations
I, Trans. Amer. Math. Soc. 275: 1-36 (1983).

[13] Douglas Hoover and Edwin Perkins, Nonstandard construction of the
stochastic integral and applications to stochastic differential equations
II, Trans. Amer. Math. Soc. 275:37-58 (1983).

[12] Priscilla Greenwood and Edwin Perkins, A conditioned limit theorem for
random walk, and Brownian local time on square root boundaries, Annals of
Probability 11:227-261 (1983).

[11] Edwin Perkins, The Hausdorff dimension of the Brownian slow points, in
Z. fur Wahrscheinlichkeitstheorie 64:369-399 (1983).

[10] Michel Emery and Edwin Perkins, La filtration de B + L, Z. fur Wahr.
59:383-390 (1982).

[9] Edwin Perkins, Local time is a semi-martingale, Z. fur Wahr. 60:79-117
(1982).

[8] Edwin Perkins, Local time and pathwise uniqueness for stochastic
differential equations, in Seminaire de Probabilities XVI, Lect. Notes in
Math 920, Springer 201-208 (1982).

[7] Edwin Perkins, Weak invariance principles for local time, Z. fur
Wahr., 60: 437-451 (1982).

[6] Edwin Perkins, On the construction and distribution of a local
martingale with a given absolute value, Trans. Amer. Math. Soc. 271:261-281
(1982).

[5] Edwin Perkins, On the iterated logarithm law for local time,
Proc. Amer. Math. Soc. 81, 470-472 (1981).

[4] Edwin Perkins, On the uniqueness of a local martingale with a given
absolute value, Z. fur Wahr. 56, 255-281 (1981).

[3] R.V. Chacon, Y. LeJan, E. Perkins, S.J. Taylor, Generalized arc length
for Brownian motion and Levy processes, Z. fur Wahr. 57, 197-211 (1981).

[2] Edwin Perkins, A global intrinsic characterization of local time,
Annals of Probabilty 9, 800-817 (1981).

[1] Edwin Perkins, The exact Hausdorff measure of the level sets of
Brownian motion, Z. fur Wahr. 58, 373-388 (1981).

Books

[1] Edwin Perkins, Dawson-Watanabe Superprocess and Measure-Valued
Diffusions
, Proceedings of the 1999 Saint Flour Summer School in
Probability, Lect. Notes in Math. 1781, pp.132--329 (2002).

Articles

[1] Edwin Perkins, Kiyosi Ito, Inaugural Recipient of the Gauss Prize 2006,
CMS Notes, March (2007).


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