Publications
Publications
[107] Ted Cox and Edwin Perkins
[106] Jean-Francois Le Gall and Edwin Perkins
[105] Manuel Cabezas, Alexander Fribergh, Mark Holmes and Edwin Perkins
[104] Nicholas J.A. Harvey, Christopher Liaw, Edwin A. Perkins and
Sikander Randhawa [103] Ted Cox and Edwin A. Perkins Rescaling the spatial lambda Fleming-Viot process [102] Jieliang Hong, Leonid Mytnik and Edwin A. Perkins On the topological boundary [102b] Jieliang Hong, Leonid Mytnik and Edwin A. Perkins [101] Mark Holmes and Edwin A. Perkins On the range of lattice models [100] Thomas Hughes and Edwin A. Perkins On the boundary of the zero set [99] Leonid Mytnik and Edwin A. Perkins The dimension of the boundary [98] Spencer Frei and Edwin A. Perkins A lower bound for $p_c$ in range-R [97] Carl Mueller, Leonid Mytnik and Edwin A. Perkins On the boundary of the support of [96] Remco van der Hofstad, Mark Holmes and Edwin A. Perkins Criteria for convergence [95] Ted Cox and Edwin A. Perkins A complete convergence theorem [94] Carl Mueller, Leonid Mytnik, and Edwin A. Perkins Nonuniqueness for a parabolic SPDE with 3/4-epsilon diffusion coefficients
, Ann. Prob. 42, 2032-2112 (2014). [93] Steven P. Lalley, Edwin A. Perkins, and Xinghua Zheng [92] Ted Cox Richard Durrett, and Edwin Perkins, Voter model perturbations and [91] Richard Bass and Edwin Perkins, On uniqueness in law for parabolic SPDE's [90] Chris Burdzy, Carl Mueller and Edwin Perkins, [89] Ted Cox, Mathieu Merle and Edwin Perkins, [88] Leonid Mytnik and Edwin Perkins, Pathwise uniqueness for stochastic heat equations [87] Richard Bass and Edwin Perkins, A new technique for proving [86] Richard Bass and Edwin Perkins,
Degenerate stochastic differential [85] Ted Cox and Edwin Perkins,
Renormalization of the two-dimensional [84] Mark Holmes and Edwin Perkins,
Weak convergence of measure-valued [83] Ted Cox and Edwin Perkins, Survival and coexistence in [82] Donald Dawson and Edwin Perkins, On the uniqueness problem for [81] Leonid Mytnik, Edwin Perkins and Anja
Sturm, On pathwise uniqueness for [80] Siva Athreya, Richard Bass, Maria Gordina
and Ed Perkins, [79] Richard Durrett, Leonid Mytnik and Ed
Perkins, Competing [78] Richard Bass and Edwin Perkins, Countable
systems of degenerate [77] Ted Cox and Ed Perkins, Rescaled
Lotka-Volterra models converge to [76] Siva Athreya, Richard Bass and Edwin
Perkins, Holder
norm [75] Ted Cox and Ed Perkins, An application of the voter [74] Ed Perkins, Super-Brownian motion and criticial spatial stochastic
systems, [73] Leonid Mytnik and Ed Perkins, Regularity
and irregularity of [72] Richard Bass and Edwin Perkins, Degenerate
stochastic differential [71] Don Dawson, Alison Etheridge, Klaus
Fleischmann, Leonid Mytnik, Ed [70] Don Dawson, Alison Etheridge, Klaus
Fleischmann, Leonid Mytnik, Ed [69] Siva Athreya, Martin Barlow, Richard Bass,
Ed Perkins, Degenerate [68] Don Dawson, Klaus Fleischmann, Leonid
Mytnik, Ed Perkins and Jie [67] Richard Bass and Edwin Perkins, On the
martingale problem for [66] Ted Cox, Achim Klenke and Edwin Perkins,
Weak convergence and [65] Carl Mueller and Edwin Perkins, Extinction
for two parabolic PDE's [64] Ted Cox, Richard Durrett and Edwin
Perkins, Rescaled Voter Models [63] Ted Cox, Richard Durrett and Edwin
Perkins, Rescaled Particle [62] Donald Dawson and Edwin Perkins,
Measure-valued processes [61] Donald Dawson and Edwin Perkins, Long-time Behaviour
and [60] Steven Evans and Edwin Perkins, Collision
local times, historical [59] Richard Durrett and Edwin Perkins, Rescaled Contact
Processes [58] Edwin A. Perkins and S. James Taylor, The multifractal
[57] Donald Dawson and Edwin Perkins, Measure-valued processes
[56] Hassan Allouba, Richard Durrett, John Hawkes and Edwin
Perkins, [55] Martin Barlow, Robin Pemantle and Edwin Perkins, DLA on [54] Donald Dawson and Edwin Perkins, Measure-valued processes
and [53] Edwin Perkins, On the martingale problem for interactive [52] J.F. Le Gall and Edwin Perkins, The exact Hausdorff
measure of [51] J.F. Le Gall, Edwin Perkins and S.J. Taylor, The packing [50] Steven N. Evans and Edwin Perkins, Explicit stochastic
integral [49] Steve Evans and Edwin Perkins, Measure-valued branching
diffusions [48] Martin Barlow and Edwin Perkins, On the filtration of
historical Brownian [47] Edwin Perkins, On the strong Markov property of the
support of [46] Edwin Perkins, Measure-valued
diffusions and interactions, Proceedings of [45] Carl Mueller and Edwin Perkins, The compact support
property for [44] Edwin Perkins, Measure-valued branching diffusions with
spatial [43] Edwin Perkins, Conditional Dawson-Watanabe processes and
Fleming-Viot [42] Don Dawson and Edwin Perkins, Historical processes.
Memoirs of the [41] Martin Barlow, Steven Evans and Edwin Perkins, Collision
local times [40] On the continuity of measure-valued processes, Seminar on
Stochastic [39] Steve Evans and Edwin Perkins, An absolute continuity
result for [38] Steven Evans and Edwin Perkins, Measure-valued Markov
branching [37] Edwin Perkins, Polar sets and multiple points for
super-Brownian [36] Martin Barlow and Edwin Perkins, On pathwise uniqueness
and expansion [35] Martin Barlow and Edwin Perkins, Symmetric Markov chains
in Zd: How [34] Donald Dawson, Ian Iscoe and Edwin Perkins,
Super-Brownian motion: [33] Martin Barlow and Edwin Perkins, Sample path properties
of stochastic [32] Edwin Perkins, The exact Hausdorff measure of the closed
support of [31] Edwin Perkins and S. James Taylor, Measuring close
approaches on a [30] Edwin Perkins, A space-time property of a class of
measure-valued [29] Martin Barlow and Edwin Perkins, Brownian motion on the
Sierpinski [28] Edwin Perkins and S. James Taylor, Uniform Hausdorff
measure results [27] Martin Barlow, Edwin Perkins, S. James Taylor, Two
uniform intrinsic [26] Martin Barlow and Edwin Perkins, The behaviour of
Brownian motion at a [25] Martin Barlow, Edwin Perkins, S. James Taylor, The
behaviour and [24] Edwin Perkins, On the continuity of the local time of
stable processes, [23] Edwin Perkins, The Cereteli-Davis H1-embedding theorem and an optimal [22] Edwin Perkins, Multiple Stochastic Integrals - A
Counter-example, [21] Burgess Davis and Edwin Perkins, On Brownian slow points
- the [20] Martin Barlow and Edwin Perkins, Levels at which every
Brownian [19] Martin Barlow and Edwin Perkins, One dimensional
stochastic [18] Priscilla Greenwood and Edwin Perkins, Limit theorems for
excursions [17] Edwin Perkins, Stochastic integrals and progressive
measurability - an [16] Edwin Perkins, Stochastic processes and nonstandard
analysis, Vol. 983, [15] Martin Barlow and Edwin Perkins, Strong Existence,
Uniqueness and [14] Douglas Hoover and Edwin Perkins, Nonstandard
construction of the [13] Douglas Hoover and Edwin Perkins, Nonstandard
construction of the [12] Priscilla Greenwood and Edwin Perkins, A conditioned
limit theorem for [11] Edwin Perkins, The Hausdorff dimension of the Brownian
slow points, in [10] Michel Emery and Edwin Perkins, La filtration de B + L,
Z. fur Wahr. [9] Edwin Perkins, Local time is a semi-martingale, Z. fur
Wahr. 60:79-117 [8] Edwin Perkins, Local time and pathwise uniqueness for
stochastic [7] Edwin Perkins, Weak invariance principles for local time,
Z. fur [6] Edwin Perkins, On the construction and distribution of a
local [5] Edwin Perkins, On the iterated logarithm law for local
time, [4] Edwin Perkins, On the uniqueness of a local martingale
with a given [3] R.V. Chacon, Y. LeJan, E. Perkins, S.J. Taylor,
Generalized arc length [2] Edwin Perkins, A global intrinsic characterization of
local time, [1] Edwin Perkins, The exact Hausdorff measure of
the level sets of Books [1] Edwin Perkins, Dawson-Watanabe
Superprocess and Measure-Valued Articles [1] Edwin Perkins, Kiyosi Ito, Inaugural Recipient of the Gauss Prize 2006,
A complete convergence theorem for the q-voter model
and other voter model perturbations in two dimensions , submitted, 80 pages (2023).
A stochastic differential equation for local times of super-Brownian motion
, submitted, 36 pages (2023).
Historical lattice trees , to appear Comm. Math. Phys., 63 pages (2022).
Optimal anytime regret with two experts , FOCS 2020, p.1404--1415 (2020)
[journal version to
appear in Mathematical Statistics and Learning (36 pp.) (2023)].
and convergence to
super-Brownian motion , Elect. J. Prob. 25, 1--56 (2020).
of the range of super-Brownian motion
, Ann. Prob. 48, 1168--1201 (2020).
of the range of super-Brownian motion:Supplementary
Materials
in high dimensions
, Prob. Th. Rel Fields 176, 941-1009 (2020).
of super-Brownian motion
, Ann Inst. Henri Poincare 55, 2395-2422 (2019).
of super-Brownian motion
, Prob. Th. Rel. Fields 174, 821-885 (2019).
percolation in two and three dimensions
, Elect. J. Prob. 21, (22 pages) (2016).
super-Brownian motion: with appendices
, Ann. Prob. 45, 3482--3534 (2017).
to super-Brownian motion on path space
, Ann. Prob. 45, 278--376 (2017).
for voter model perturbations
, Ann. Appl. Prob. 24, 150--197 (2014).
reaction diffusion equations
, Asterisque 349, 113 pp, 2013.
and infinite dimensional SDE's
, Elect. J. Prob. 17, 54 pages (2012).
Non-uniqueness for non-negative solutions of parabolic SPDE's
,
Burkholder volume of the Ill.J. Math 54, 1481-1507 (2010).
Co-existence in a two-dimensional Lotka-Volterra model
,
Elect. J. Probability 15, 1190--1266 (2010).
with Holder continuous coefficients: the white noise case
,
Prob. Th. Rel. Fields 149, pp. 1--96 (2011).
uniqueness for martingale problems , 9 pages,
to appear in Tribute to Jean-Michel Bismut,
Eds. R. Leandre, X. Ma, W. Zhang, Asterisque (2009).
equations arising from
catalytic branching networks
,
Elect. J. Probability 13, 1808-1885 (2008).
Lotka-Volterra Model,
Ann. of Applied Probability 18, 747-812 (2008).
processes and r-point functions,
Ann. Probability 35, 1769-1782 (2007).
stochastic spatial Lotka-Volterra models,
Prob. Theory and Rel. Fields 139, 89-142 (2007).
catalytic branching networks and other singular diffusions,
Illinois J. Math 50, 323-383 (2006).
stochastic heat equations with non-Lipschitz coefficients, Ann.
Probability 34, 1910-1959 (2006).
Infinite-dimensional sde's of Ornstein-Uhlenbeck type, Stoch.
Proc. Appl. 116, 381-406 (2006).
super-Brownian motions as limits of interacting particle systems,
Elect. J. Probability 10, 1147-1220 (2005).
stochastic differential equations with applications to
super-Markov
chains, Elect. J. Prob. 9, 634-673
(2004).
super-Brownian motion,
Ann. Prob. 33, 904-947 (2005).
estimates for elliptic operators on finite and infinite
dimensional
spaces, Trans. Amer. Math.
Soc. 357, 5001-5029 (2005).
model-super-Brownian motion invariance principle, Ann. Inst.
Henri Poincare' 40, 25-32 (2004).
Bull. Can. Math. Soc. 47, 280--297
(2004).
densities for stable branching superprocesses,
Ann. Prob. 31, 1413--1440 (2003).
equations with Holder continuous coefficients and super-Markov chains,
Trans. Amer. Math. Soc.
355, 373--405 (2002).
Perkins and Jie Xiong, Mutually catalytic super-Brownian motion
in the
plane, Ann. Prob. 30, 1681--1762 (2002).
Perkins and Jie Xiong, Mutually catalytic branching in the plane:
infinite measure states, Elect. J. Probability 7 (64 pages)
(2002).
Stochastic differential equations and super-Markov chains,
Prob. Theory Rel. Fields 123, 484--520 (2002).
Xiong, Mutually catalytic super-Brownian branching in the plane:
uniqueness Ann. Inst. Henri Poincar\'e Prob. et Stat. 39,
135-191 (2003).
Super-Brownian motion, Seminaire de Probabilite's XXXV, 195-201
(2001)
linear systems duality, Proceedings of the International
Conference on
Stochastic Models, 1998, CMS Conference Proceedings, 26, 41-66
(2000).
on the lattice, Ann. Inst. Henri Poincare. Prob. et Stat. 36,
301-338 (2000).
Converge to Super-Brownian Motion, Ann. Prob., 28, 185-234
(2000).
Systems Converging to Super-Brownian Motion, pp. 269-284,
Perplexing
Problems in Probability--Festschrift in Honor of Harry Kesten
(1999).
and renormalizaton of branching particle systems pp 45-106
Stochastic
pde's:Six Perspectives, AMS Math. Surveys and Monographs (1999).
co-existence in a
mutually catalytic branching model (49 pages),
Annals Prob. 26, 1088-1138 (1998).
stochastic
calculus and competing superprocesses (125 pages), Elect. J.
Prob., March, 1998.
Converge to
Super-Brownian Motion for d greater than or equal to 2,
Prob. Theory and Related Fields 114, 309-399 (1999).
spectrum of
super-Brownian motion, Annales d'Institut Henri Poincare 34,
97-138 (1998).
and renormalizaton of branching particle systems (to appear in
Stochastic pde's:Six Perspectives, AMS Math. Surveys and
Monographs) (63 pages)
(1997).
Super-tree random
measures, J. Theoretical Probability 10, 773-794 (1997).
a binary tree,
Prob. Theory and Rel. Fields 107, 1-60 (1997).
stochastic partial differential equations, Can. J. Math., Volume
of Invited
papers for 50th Anniversary of the CMS, 19-60 (1996).
measure-valued branching diffusions, Memoirs of the American
Math. Soc. 115,
No. 549, 1-89 (1995).
two-dimensional super-Brownian motion, Annals of Prob.
23,1719-1747 (1995).
measure of super-Brownian motion, Stoch. Proc. Appl. 59, 1-20
(1995).
representations for superprocesses, Annals of Prob. 23, 1772-1815
(1995).
with singular interactions, Can. J. Math. 46, 120-168 (1994).
motion, Annals of Prob. 22, 1273-1294 (1994).
super-Brownian motion, in The Dynkin Festschrift, M. Freidlin
(ed.) 307-326
(1994).
the I.C.M., Zurich,1036-1046 (1995).
solutions to the heat equation with noise, Prob. Theory and
Related Fields
93, 325-358 (1992).
interactions, Prob. Theory and Related Fields 94, 189-245 (1992).
processes, Seminar on Stochastic Processes 1991, 143-156, Ed. E. Cinlar,
K.L. Chung R.K. Getoor (1991).
Amer. Math. Soc., 93, no. 454, 179 pages (1991).
and measure-valued processes, Can. J. Math. 43, 897-938 (1991).
Processes 1990, E. Cinlar, P.J. Fitzsimmons and R.J. Williams
(eds.)
261-268 (1991).
measure-valued diffusions and applications, Trans. Amer. Math.
Soc. 325,
661-682 (1991).
processes conditioned on non-extinction, Israel J. Math 71,
329-337 (1990).
motion, Ann. Probability 18 453-491 (1990).
of filtrations. Seminaire de Probabilities XXIV, J. Azema,
P.A. Meyer, M.
Yor (eds.), 194-209 (1990).
fast can they move? Prob. Theory and Related Fields 82,
95-108 (1989).
path properties and hitting probabilities. Prob. Theory and
Related Fields
83, 135-206 (1989).
integrals and stochastic differentiation, Stochastics 27, 261-293
(1989).
super-Brownian motion. Annales de l'Institut Henri
Poincare, 25, 205-224
(1989).
Brownian path, Annals of Probability 16, 1458-1480 (1988).
diffusions, Trans. Amer. Math. Soc. 305, 743-796 (1988).
gasket, Prob. Theory and Related Fields, 79, 543-623 (1988).
for stable processes, Probability Theory and Related Fields
(formerly
Z.F.W.) 76, 257-289 (1987).
constructions for the local time of a class of Levy processes,
Ill. J.
Math., 30, 19-65 (1986).
slow point, Trans. Amer. Math. Soc., 296, 741-775 (1986).
construction of local times for Levy processes, Seminar on
Stochastic
Processes, 1984, 23-54, ed. E. Cinlar, Birkhauser (1986).
Seminar on Stochastic Processes, 1984, 151-164, ed. E. Cinlar,
Birkhauser
(1986).
embedding in Brownian motion,
Seminar on Stochastic Processes 1985, 172-223, Ed. E. Cinlar,
K.L. Chung R.K. Getoor (1986).
Seminaire de Probabilities XIX, Lect. Notes in Math 1123,
Springer 258-262
(1985).
critical cases, Annals of Probability 13, 774-803 (1985).
excursion is exceptional, Seminaire de Probabilities XVIII, Lect.
Notes in
Math 1059 Springer 1-28 (1984).
differential equations involving a singular increasing process,
Stochastics
Vol. 12 229-249 (1984).
from a moving boundary, Theory of Probability and its
Applications 29
517-528 (1984).
example, Seminaire de Probabilites XVII, Lect. Notes in Math.
986,
Springer, 67-71 (1983).
Springer, 162-185 (1983).
Non-uniqueness in an equation involving local time, Seminaire de
Probabilites XVII, Lect. Notes in Math. 986, Springer, 32-61
(1983).
stochastic integral and applications to stochastic differential
equations
I, Trans. Amer. Math. Soc. 275: 1-36 (1983).
stochastic integral and applications to stochastic differential
equations
II, Trans. Amer. Math. Soc. 275:37-58 (1983).
random walk, and Brownian local time on square root boundaries,
Annals of
Probability 11:227-261 (1983).
Z. fur Wahrscheinlichkeitstheorie 64:369-399 (1983).
59:383-390 (1982).
(1982).
differential equations, in Seminaire de Probabilities XVI, Lect.
Notes in
Math 920, Springer 201-208 (1982).
Wahr., 60: 437-451 (1982).
martingale with a given absolute value, Trans. Amer. Math. Soc.
271:261-281
(1982).
Proc. Amer. Math. Soc. 81, 470-472 (1981).
absolute value, Z. fur Wahr. 56, 255-281 (1981).
for Brownian motion and Levy processes, Z. fur Wahr. 57, 197-211
(1981).
Annals of Probabilty 9, 800-817 (1981).
Brownian motion, Z. fur Wahr. 58, 373-388 (1981).
Diffusions, Proceedings of the 1999
Saint Flour Summer School in
Probability, Lect. Notes in Math. 1781, pp.132--329 (2002).
CMS Notes, March (2007).
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