Cutting Brownian paths Memoir AMS, 95pp.,
Number 657, Volume 137,
American Mathematical Society,
Providence, RI, January 1999
(with R. Bass)
Math review 99g:60146
Seminar on Stochastic Processes 1992,
276pp., Birkhäuser, Boston 1993
(managing editor, with R. Bass)
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Multidimensional Brownian Excursions and
Potential Theory, 172pp. Longman, London 1987
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Research articles
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(preprint, with T. Beck, B. Brandolini, A. Henrot, J. Langford, S. Larson, R. Smits and S. Steinerberger)
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Protecting billiard balls from collisions (preprint, with J. Athreya)
(Math ArXiv version)
Bounds on the probability of radically different opinions (preprint, with J. Pitman)
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Simultaneous boundary hitting by coupled reflected Brownian motions
Electron. Comm. Probab.24 (2019) paper no. 22
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(Math ArXiv version)
On pinned billiard balls and foldings
(preprint, with J. Athreya and M. Duarte)
(Math ArXiv version)
On the number of hard ball collisions
J. London Math. Soc.
(to appear, with M. Duarte)
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A lower bound for the number of elastic collisions
Comm. Math. Phys. (to appear, with M. Duarte)
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Knudsen gas in flat tire
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Inverse exponential decay: Stochastic fixed point equation and ARMA models
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Twin peaks
Random Structures Algorithms (to appear, with S. Pal)
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The Hinge Region Strengthens the Nonspecific Interaction between Lac-Repressor and DNA: A Computer Simulation Study.
PLoS ONE 11(3): e0152002.
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Random reflections in a high dimensional tube
J. Theoret. Probab.31 (2018) 466-493
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Obliquely reflected Brownian motion in non-smooth planar domains
Ann. Probab.45 (2017) 2971-3037
(with Z. Chen, D. Marshall and K. Ramanan)
Gravitation versus Brownian motion
Ann. I. H. Poincaré
(to appear, with S. Banerjee and M. Duarte)
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Method for the analysis of contribution of sliding and hopping to a
facilitated diffusion of DNA-binding protein: Application to in vivo
data Phys. Rev. E92, 022721, August 2015
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Reflections on reflections. in Stochastic Analysis. A Series of Lectures.
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The distribution of the spine of a Fleming-Viot type process
Stoch. Process. Appl.128 (2018) 3751-3777
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Can one make a laser out of cardboard?
Ann. Appl. Probab.27 (2017) 1951-1991
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Stirring two grains of sand
Electr. J. Probab.20 (2015) 1-29, article 13.
A random flight process associated to a Lorentz gas with variable density in a gravitational field
Stoch. Process. Appl.128 (2018) 79-107
(with D. Rizzolo)
Meteor process on ${\mathbb Z}^d$
Probab. Theory Rel. Fields163 (2015) 667-711.
Comparison of quenched and annealed invariance principles for random conductance model: Part II.
A Festschrift in Honor
of Masatoshi Fukushima.
59--83, Interdiscip. Math. Sci., 17, World Sci. Publ., Hackensack, NJ, 2015.
(with M. Barlow and A. Timar)
On meteors, earthworms and WIMPs
Ann. Appl. Probab. 25 (2015) 1729-1779
(with S. Billey, S. Pal and B. Sagan)
Fractal trace of earthworms
Phys. Rev. E87 no. 5, May 2013
(with R. Holyst and L. Pruski)
Comparison of quenched and annealed invariance principles for random conductance model
Probab. Theory Rel. Fields164 (2016) 741-770 (with M. Barlow and A. Timar)
Forward Brownian motion
Probab. Theory Rel. Fields160 (2014) 95-126
(with M. Scheutzow)
Joint convergence along different subsequences of the signed cubic
variation of fractional Brownian motion
Probab. Theory Rel. Fields159 (2014) 237-272
(with D. Nualart and J. Swanson)
Permutations with given peak set
Journal of Integer Sequences 16 (2013)
Article 13.6.1
(with S. Billey and B. Sagan)
Rubber bands, pursuit games and shy couplings
Proc. London Math. Soc. 109 (2014) 121-160
(with M. Bramson and W. Kendall)
Invisibility via reflecting coating
J. London Math. Soc. 88 (2013) 359-374
(with T. Kulczycki)
Deterministic approximations of random reflectors
Trans. Amer. Math. Soc.365 (2013) 6367-6383
(with O. Angel and S. Sheffield)
Extinction of Fleming-Viot-type particle systems with strong drift
Electron. J. Probab. 17 (2012), paper 11, 1-15
(with M. Bieniek and S. Pal)
Reflecting random walk in fractal domains
Ann. Probab.41 (2013) 2791-2819
(with Z. Chen)
Brownian earthworm
Ann. Probab.41 (2013) 4002-4049
(with Z. Chen and S. Pal)
Isolated zeros for Brownian motion with variable drift
Electron. J. Probab. 16 (2011), paper 65, 1793-1815
(with T. Antunovic, Y. Peres and J. Ruscher)
Stationary distributions for jump processes with memory
Ann. I. H. Poincaré 48 (2012) 609-630
(with T. Kulczycki and R. Schilling)
Stationary distributions for jump processes with inert drift,
Malliavin Calculus and Stochastic Analysis: A Festschrift in Honor
of David Nualart, Springer Proceedings in Mathematics & Statistics 34,
Springer, New York, 2013, 139-172
(with T. Kulczycki and R. Schilling)
Non-uniqueness for non-negative solutions of parabolic
stochastic partial differential equations
Illinois J. Math.,
Burkholder Volume54 (2010) 1481-1507
(with C. Mueller and
E. Perkins)
Shy Couplings, CAT(0) Spaces, and the Lion and Man
Ann. Probab.41 (2013) 744-784
(with M. Bramson and W. Kendall)
Comment on article by Robert Bayesian Analysis5 (2010) 233-236.
Crowding of Brownian spheres
ALEA Lat. Am. J. Probab. Math. Stat.7 (2010) 193-205 (with
S. Pal and J. Swanson)
Archimedes' principle for Brownian liquid
Ann. Appl. Probab.21 (2011) 2053-2074
(with Z. Chen and S. Pal)
Markov processes on time-like graphs
Ann. Probab.39 (2011) 1332-1364
(with S. Pal)
Non-extinction of a Fleming-Viot particle model
Probab. Theory Rel. Fields 153
(2012) 293-332
(with
M. Bieniek and S. Finch)
Differentiability of stochastic flow of reflected
Brownian motions
Electron. J. Probab. 14 (2009) 2182-2240.
Multiplicative functional for reflected Brownian
motion via deterministic ODE
Illinois J. Math.,
Burkholder Volume, 54 (2010) 895-925
(with J. Lee)
Stationary distributions for diffusions with inert
drift
Probab. Theory Rel. Fields146 (2010) 1-47
(with R. Bass, Z. Chen and M. Hairer)
A change of variable formula with Ito correction term
Ann. Probab.38 (2010) 1817-1869
(with J. Swanson)
The Skorokhod problem in a time-dependent interval
Stoch. Process. Appl.119 (2009) 428-452
(with W. Kang and K. Ramanan)
Markov processes with product-form stationary distribution
Electron. Comm. Probab.13 (2008) 614-627
(with D. White)
On pathwise uniqueness for reflecting Brownian motion
in $C^{1+\gamma}$ domains
Ann. Probab.36 (2008) 2311-2331
(with R. Bass)
Brownian motion with inert drift, but without flux: a
model
Physica A384 (2007) 278-284
(with R. Holyst and L. Pruski)
Discrete approximations to reflected Brownian motion
Ann. Probab.36, (2008) 698-727
(with Z. Chen)
Mirror couplings and Neumann eigenfunctions
Indiana U. Math. J.57 (2008) 1317-1353.
(with R. Atar)
Pathwise uniqueness for a degenerate stochastic
differential equation
Ann. Probab.35, (2007) 2385-2418
(with R. Bass and Z. Chen)
Pathwise uniqueness for two dimensional reflecting
Brownian motion in certain planar Lipschitz domains
Electr. Comm. Probab.11 (2006) paper 18, pages 178-181.
(with R. Bass)
Shy couplings
Probab. Theory Rel. Fields137 (2007) 345-377.
(with I. Benjamini and Z. Chen)
Comparison of potential theoretic properties of rough
domains Proc. AMS 134 (2006), 3247-3253.
(with Z. Chen)
On the Robin problem in fractal domains
Proc. London Math. Soc.96 (2008), 273-311
(with R. Bass and Z. Chen)
An annihilating-branching particle model for the heat
equation with average temperature zero
Ann. Probab.34, (2006) 2382-2405
(with J. Quastel)
Synchronous couplings of reflected Brownian motions in
smooth domains Illinois J. Math., Doob Volume50 (2006) 189-268
(with Z. Chen and P. Jones)
Neumann eigenfunctions and Brownian couplings
Potential theory in Matsue.
Proceedings of the International Workshop on Potential Theory,
Matsue 2004. Advanced Studies in
Pure Mathematics 44. Mathematical Society of Japan, 2006,
pp. 11-23
(review paper)
A Gaussian oscillator Electron. Comm. Probab. 9
(2004), paper 10, pp. 92-95 (with D. White)
The "hot spots" problem in planar domains with one
hole. Duke Math. J.129 (2005) 481-502
The heat equation in time dependent domains with
insulated boundaries J. Math. Anal. Appl. 294 (2004)
581-595
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Coalescence on the high-dimensional sphere: a
caricature for perfect simulation. Symposium in Honour of Ole
E. Barndorff-Nielsen (Aarhus, 2000), 50-52, Memoirs, 16, Univ.
Aarhus, Aarhus, 2000 (with W. Kendall)
Traps for reflected Brownian motion
Math. Z.252 (2006) 103-132
(with Z. Chen and D. Marshall)
The heat equation and reflected Brownian motion
in time dependent domains. II. Singularities of solutions
J. Func. Anal.204 (2003) 1-34
(with Z. Chen and J. Sylvester)
Lenses in skew Brownian flow
Ann. Probab. 32 (2004) 3085-3115
(with H. Kaspi)
Stochastic differential equations driven by stable
processes for which pathwise uniqueness fails
Stoch. Proc. and their Appl.111 (2004) 1-15
(with R. Bass and Z. Chen)
Erratum to "The supremum of Brownian local times on Hölder curves"
Ann. I. H. Poincaré 38 (2002) 799-800 (with
R. Bass)
Super-Brownian motion with reflecting historical
paths. II. Convergence of approximations
Probab. Theory Rel. Fields133 (2005) 145-174
(with L. Mytnik)
Uniqueness for reflecting Brownian motion in lip domains
Ann. I. H. Poincaré 41 (2005) 197-235
(with R. Bass and Z. Chen)
On nodal lines of Neumann eigenfunctions
Electron. Comm. Probab. 7, (2002)
paper 14, p. 129-139
(with R. Atar)
On Neumann eigenfunctions in lip domains
Journal AMS 17 (2004) 243-265
(with R. Atar)
Shocks and business cycles Advances in Theoretical
Economics 5 (2005) 1-86, no. 1, article 2
(with D. Frankel)
Censored stable processes
Probab. Theory Rel. Fields127 (2003) 89-152
(with K. Bogdan and Z. Chen)
Mechanisms for facilitated target location
and the optimal number
of molecules in the diffusion search process
Phys. Rev. E64 (2001) article no. 011914
(with R. Holyst)
Coalescence of synchronous couplings
Probab. Theory Rel. Fields123 (2002) 553-578
(with Z. Chen)
Stable processes have thorns
Ann. Probab. 31 (2003) 170-194
(with T. Kulczycki)
Brownian motion reflected on Brownian motion
Probab. Theory Rel. Fields122 (2002) 471-493
(with D. Nualart)
The heat equation and reflected Brownian motion
in time dependent domains
Ann. Probab.32 (2004) 775-804
(with Z. Chen and J. Sylvester)
Super-Brownian motion with reflecting historical paths
Probab. Theory Rel. Fields121 (2001) 447-491
(with J.-F. Le Gall)
The supremum of Brownian local times on Hölder curves
Ann. Inst. Henri Poincaré 37 (2001) 627-642
(with R. Bass)
Reduction of dimensionality in a diffusion
search process and kinetics of gene expression
Physica A, 277 (2000) 71-82) (with R. Holyst,
M. Blazejczyk, G. Goralski and L. Bocquet)
Coalescence of skew Brownian motions
Seminaire de Probabilites XXXV, LNM 1755
(2001) 202-205
(with M. Barlow, H. Kaspi and A. Mandelbaum)
A Fleming-Viot particle representation of Dirichlet Laplacian
Comm. Math. Phys.214 (2000) 679-703
(with R. Holyst and P. March)
Diffusion on curved periodic surfaces
Phys. Rev. E 60 (1999) 302-307
(with R. Holyst, D. Plewczynski
and A. Aksimentiev)
Fiber Brownian motion and the `hot spots' problem
Duke Math. J.105 (2000) 25-58
(with R. Bass)
Math review 2001g:60190
Local time flow related to skew Brownian motion
Ann. Probab.29 (2001) 1693-1715
(with Z.-Q. Chen)
Variably skewed Brownian motion
Electr. Comm. Probab. 5, (2000)
paper 6, p. 57-66.
(with M. Barlow, H. Kaspi and A. Mandelbaum)
Math review 2001j:60146
Weak convergence of reflecting Brownian motions
Electr. Comm. Probab. 3, (1998)
paper 4, p. 29-33
(with Z.-Q. Chen)
Math review 99d:60091
Efficient Markovian couplings: examples and counterexamples
Ann. Appl. Probab.10 (2000)
362-409. (with W. Kendall)
A counterexample to the "hot spots" conjecture
Ann. Math.149 (1999) 309-317
(with W. Werner)
Math review 2000b:35044
Stochastic bifurcation models
Ann. Probab.27 (1999) 50-108
(with R. Bass)
Math review 2000b:60201
On minimal parabolic functions and time-homogeneous
parabolic $h$-transforms
Trans. Amer. Math. Soc. 351 (1999)
3499-3531
(with T. Salisbury)
Math review 99m:60113
Positivity of Brownian transition densities
Electr. Comm. Probab. 2 (1997)
paper 4, p. 41-53
(with M. Barlow and R. Bass)
Math review 99e:60166
On the time and direction of stochastic
bifurcation.
In
Asymptotic Methods in Probability and Statistics.
A Volume in Honour of Miklos Csorgo.
B. Szyszkowicz, ed., pp. 483-500.
Elsevier, Amsterdam, 1998.
(with D. Frankel and A. Pauzner)
Math review 99k:60148
Brownian motion in a Brownian crack
Ann. Appl. Probab. 8 (1998) 708-748
(with D. Khoshnevisan)
Math review 99g:60147
On the "hot spots" conjecture of J. Rauch
J. Func. Anal.164 (1999) 1-33
(with R. Bañuelos)
Math review 2000m:35085
Fast equilibrium selection by rational
players living in a changing world
Econometrica 69 (2001) 163-190
(with D. Frankel and A. Pauzner)
Sets avoided by Brownian motion
Ann. Probab.26 (1998) 429-464
(with O. Adelman and R. Pemantle)
Math review 99i:60152
Configurational transition in a Fleming-Viot-type model
and probabilistic interpretation of Laplacian eigenfunctions
J. Phys. A 29, 1996, 2633-2642.
(with R. Holyst, D. Ingerman and P. March)
Eigenvalue expansions for
Brownian motion with an application to occupation times,
Electronic Journal of Probability 1, 1996,
Paper 3,
1-19. (with R. Bass)
Math review 97c:60201
A critical case for Brownian slow points
Probab. Th. Rel. Fields 105, 1996, 85-108.
(with R. Bass)
Math review 97m:60054
The level sets of iterated Brownian motion
Seminaire de Probabilites XXIX, J. Azéma,
M. Emery, P.A. Meyer, M. Yor, eds., 1995, 231-236.
(with D. Khoshnevisan)
Math review 98k:60138
No triple point of planar Brownian motion
is accessible Ann. Probab. 24, 1996, 125-147
(with W. Werner)
Math review 97j:60147
Ito formula for an asymptotically
4-stable process Ann. Appl. Probab. 6,
1996, 200-217 (with A. Madrecki)
Math review 99a:60042
Sur quelques filtrations et transformations
browniennes Seminaire de Probabilites XXIX, J. Azéma,
M. Emery, P.A. Meyer, M. Yor, eds., 1995, 56-69.
(with S. Attal, M. Émery and Y. Hu)
Math review 98j:60111
Iterated law of iterated logarithm
Ann. Probab. 23, 1995, 1627--1643
(with J. San Martin)
Math review 97d:60075
Labyrinth dimension of Brownian trace
(invited paper) Probability and Mathematical Statistics.
Volume Dedicated to the Memory of Jerzy Neyman. 15,
1995, 165-193.
Math review 97j:60146
Conditioned Brownian motion in planar domains
Probab. Th. Rel. Fields 101, 1995, 479-493
(with R. Bass)
Math review 96b:60199
2-D Brownian motion in a system of reflecting barriers:
effective diffusivity by a sampling method
J. Phys. A: Math. General 27, 1994, 631-644.
(with R. Holyst and D. Ingerman)
An asymptotically 4-stable process
J. Fourier Anal. Appl. Special Issue.
Proceedings of the Conference in Honor of J.-P. Kahane,
1995, 97-117. (with A. Madrecki)
Math review 96j:60072
A Skorohod-type lemma and a decomposition
of reflected Brownian motion Ann. Probab. 23,
1995, 586-604 (with E. Toby)
Math review 96i:60045
Excursion laws and exceptional points
on Brownian paths. Seminaire de Probabilites XXVII,
J. Azéma, P.A. Meyer,
M. Yor, eds., Springer, Berlin, 1993, 177-181.
Math review 95m:60118
Variation of iterated Brownian motion.
Measure-Valued
Processes, Stochastic Partial Differential Equations
and Interacting Systems, D.A. Dawson, ed.,
CRM Proceedings and Lecture Notes
5, 1994, 35-53.
Math review 95h:60123
On domain monotonicity of the Neumann heat
kernel. J. Func. Anal. 116, 1993, 215-224
(with R. Bass)
Math review 94k:60120
Some path properties of iterated Brownian motion.
Seminar on Stochastic Processes 1992 K.L. Chung, E. Cinlar
and M.J. Sharpe, eds., Birkhäauser, Boston, 1993, 67-87.
Math review 95c:60075
Intersection local time for points of infinite multiplicity.
Ann. Probab. 22, 1994, 566-625
(with R. Bass and D. Khoshnevisan)
Math review 95j:60118
A three-dimensional Brownian path reflected
on a Brownian path is a free Brownian path.
Letters Math. Phys. 27, 1993, 239-241
Math review 94c:60132
2-D Brownian motion in a system of traps:
Application of conformal transformations.
J. Phys. A: Math. General 25, 1992, 2463-2471
(with R. Holyst and T. Salisbury)
The boundary Harnack principle for non-divergence form
elliptic operators. J. London Math. Soc. 50, 1994, 157-169
(with R. Bass)
Math review 95f:35058
Non-polar points for reflected Brownian motion.
Ann. Inst. Henri Poincaré 29, 1993, 199-228
(with D. Marshall)
Math review 94g:60152
The Martin boundary in non-Lipschitz domains.
Trans. Amer. Math. Soc. 337, 1993, 361-378
(with R. Bass)
Math review 93g:31019
Hölder domains and the boundary Harnack principle.
Duke Math. J. 64, 1991, 195-200
(with R. Bañuelos and R. Bass)
Math review 92g:35077
Hitting a boundary point with reflected Brownian motion.
Seminaire de Probabilites XXVI, J. Azéma, P.A. Meyer,
M. Yor, eds., 1992, 81-94. (with D. Marshall)
Math review 94g:60151
Lifetimes of conditioned diffusions.
Probab. Th. Rel. Fields 91, 1992, 405-443.
(with R. Bass)
Math review 93e:60155
A boundary Harnack principle in twisted Hölder domains.
Ann. Math. 134, 1991, 253-276 (with R. Bass)
Math review 92m:31006
Rigorous exponent inequalities for random walks.
J. Phys. A: Math. Gen. 23, 1990, L23-L28
(with G. Lawler)
Math review 91a:60271
A probabilistic proof of the boundary Harnack principle.
Seminar on Stochastic Processes 1989 K.L. Chung, E. Cinlar
and R. Getoor, eds., Birkhäuser, Boston, 1990, 1-16 (with R. Bass)
Math review 92c:60106
A representation of local time for Lipschitz surfaces.
Probab. Th. Rel. Fields 84, 1990, 521-547
(with R. Bañuelos and R. Bass)
Math review 91f:60139
On non-increase of Brownian motion. Ann. Probab.
18, 1990, 978-980.
Math review 91e:60234
Non-intersection exponents for Brownian paths. Part II.
Estimates and applications to a random fractal.
Ann. Probab. 18, 1990, 981-1009.
(with G. Lawler)
Math review 91g:60097
Non-intersection exponents for Brownian paths. Part I.
Existence and an invariance principle.
Probab. Th. Rel. Fields 84,
1990, 393-410 (with G. Lawler)
Math review 91g:60096
On the critical exponent for random walk intersections.
J. Stat. Phys. 56, 1989, 1-12
(with G. Lawler and T. Polaski)
Math review 91h:60073
Brownian crossings between spheres,
J. Math. Anal. Appl. 148, 1990,
101-120 (with J. Pitman and M. Yor)
Math review 91h:31003
Curvature of the convex hull of planar Brownian motion
near its minimum point.
Stoch. Proc. Their Appl. 33, 1989, 89-103
(with J. San Martin).
Math review 91e:60233
On Brownian excursions in Lipschitz domains. Part II.
Local asymptotic distributions,
Seminar on Stochastic Processes 1988
(E. Cinlar, K.L. Chung, R. Getoor, J. Glover,
editors), 1989, 55-85, Birkhäuser, Boston.
(with E. Toby and R.J. Williams)
Math review 90k:60142
Percolation dimension of fractals,
J. Math. Anal. Appl. 145, 1990, 282-288
Math review 90m:28007
Harmonic measure on 3-dimensional Brownian paths.
Math. Proc. Cambridge Phil. Soc. 104, 1988, 407-412
Math review 89i:60084
Geometric properties of 2-dimensional Brownian
paths. Probability Theory and Related Fields 81,
1989, 485-505
Math review 90g:60077
Minimal fine derivatives and Brownian excursions
Nagoya Math. J. 119, 1990, 115-132
Math review 92b:60067
Some asymptotic laws for crossings and excursions.
Colloque Paul Lévy sur les processus stochastiques.
Asterisque 157-158, 59-74, Paris 1988
(with J.W. Pitman and M. Yor)
Math review 90h:60070
On Brownian paths connecting boundary
points. Ann. Probab. 16, 1988, 1034-1038
Math review 89f:60086
Remarks on angular derivative.
Bull. Polish Acad. Sc. 34, 1986, 647-652
Math review 88d:30035
Convergence of 2-dimensional h-processes.
Probab. Math. Statist. 8, 1987, 49-52
Math review 89c:60094
On Brownian excursions in Lipschitz domains, I. Local path
properties. Trans. Amer. Math. Soc. 298,
1986, 289-306 (with R.J. Williams)
Math review 88g:60183
Brownian excursions and minimal thinness, III. Applications to the
angular derivative problem. Math. Z. 192,
1986, 89-107
Math review 89b:60175
Brownian excursions and minimal thinness, II. Applications to
boundary behavior of the Green function.
Seminar on Stochastic Processes 1985
(E. Cinlar, K.L. Chung, R.K. Getoor, eds.)
35-62 Birkhäuser, Boston
Math review 88h:60150
Brownian excursions and minimal thinness, I.
Ann. Probab. 15, 1987, 676-689
Math review 88h:60149
Brownian excursions from hyperplanes and smooth surfaces.
Trans. Amer. Math. Soc. 295, 1986, 35-57
Math review 87j:60118
On a theorem of Salisbury. Probab. Math.
Statist. 6, 1985, 161-166
Math review 88f:60130