**Publications**

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- Other articles are available upon request.

**Publications**

[96] Remco van der Hofstad, Mark Holmes and Edwin A. Perkins Criteria for convergence

to super-Brownian motion on path space
, 85 pages, to appear in Ann. Prob., 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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