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#### Brownian motion reflected on Brownian motion

(Springer-Verlag GmbH, 2002-04)

We study Brownian motion reflected on an "independent" Brownian path. We prove results on the joint distribution of both processes and the support of the parabolic measure in the space-time domain bounded by a Brownian path. We show that there exist
two different natural local times for a Brownian path reflected on a Brownian path.

#### On nodal lines of Neumann eigenfunctions

(Institute of Mathematical Statistics, 2002-06-03)

We present a new method for locating the nodal line of the second eigenfunction for the Neumann problem in a planar domain.

#### Coalescence of synchronous couplings

(Springer-Verlag GmbH, 2002-08)

We consider a pair of reflected Brownian motions in a Lipschitz planar domain starting from different points but driven by the same Brownian motion. First we construct such a pair of processes in a certain weak sense, since it is not known whether a strong solution to the Skorohod equation in Lipschitz domains exists. Then ...

#### Mathematical articles and bottled water

(American Mathematical Society, 2002-05)

The system for publishing mathematical articles should be reformed and the new system should resemble, on the economic side, the bottled water industry. My main theses are: (i) the results of the mathematical research should be available to the public just like tap water, (ii) the role of the commercial (and non-commercial) ...

#### Erratum to The Supremum of Brownian Times on Hölder Curves

(Birkhauser, 2002-05-21)

For [function] f [maps the set]: [0, 1] [into the set] [Real numbers], we consider L [superscript] f [subscript] t , the local time of spacetime Brownian motion on the curve f. Let S [subscript][sigma] be the class of all functions whose Hölder norm of order [sigma] is less than or equal to 1. We show that the supremum of L ...