Now showing items 32-51 of 112

    • Eigenvalue expansions for Brownian motion with an application to occupation times 

      Burdzy, Krzysztof; Bass, Richard F. (Institute of Mathematical Statistics, 1996-01-31)
      Let B be a Borel subset of R [to the power of] d with finite volume. We give an eigenvalue expansion for the transition densities of Brownian motion killed on exiting B. Let A [subscript] 1 be the time spent by Brownian ...
    • An enduring error 

      Grünbaum, Branko (2008-06-05)
    • Erratum to The Supremum of Brownian Times on Hölder Curves 

      Bass, Richard F.; Burdzy, Krzysztof (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 ...
    • Euler's ratio-sum theorem and generalizations 

      Grünbaum, Branko; Klamkin, Murray S. (2005)
      A theorem of Euler concerns sums of ratios in which Cevians of a triangle are divided by a common point. Generalizations of this result in three directions are presented: polygons instead of triangles, higher-dimensional ...
    • Excursion laws and exceptional points on Brownian paths 

      Burdzy, Krzysztof (Springer-Verlag, 1993)
      The purpose of this note is to present an example of a family of "exceptional points" on Brownian paths which cannot be constructed using an entrance law.
    • Fast equilibrium selection by rational players living in a changing world 

      Burdzy, Krzysztof; Frankel, David M.; Pauzner, Ady (The Econometric Society, 2001-01)
      We study a coordination game with randomly changing payoffs and small frictions in changing actions. Using only backwards induction, we find that players must coordinate on the risk-dominant equilibrium. More precisely, a ...
    • Fiber Brownian motion and the "hot spots" problem 

      Burdzy, Krzysztof; Bass, Richard F. (Duke University Press, 2000-10)
      We show that in some planar domains both extrema of the second Neumann eigenfunction lie strictly inside the domain. The main technical innovation is the use of "fiber Brownian motion," a process which switches between ...
    • Fibrations and Sheaves 

      Warner, Garth (2012-12-13)
      The purpose of this book is to give a systematic treatment of fibration theory and sheaf theory, the emphasis being on the foundational essentials.
    • A Fleming-Viat particle representation of Dirichlet Laplacian 

      Burdzy, Krzysztof; Holyst, Robert; March, Peter (Springer-Verlag GmbH, 2000-11)
      We consider a model with a large number N of particles which move according to independent Brownian motions. A particle which leaves a domain D is killed; at the same time, a different particle splits into two particles. ...
    • A Gaussian oscillator 

      Burdzy, Krzysztof; White, David (Institute of Mathematical Statistics, 2004-10-06)
      We present a stochastic process with sawtooth paths whose distribution is given by a simple rule and whose stationary distribution is Gaussian. The process arose in a natural way in research on interaction of an inert ...
    • Geometric Properties of 2-dimensional Brownian Paths 

      Burdzy, Krzysztof (Springer-Verlag GmbH, 1989)
      Let A be the set of all points of the plane C, visited by two-dimensional Brownian motion before time 1. With probability 1, all points of A are "twist points" except a set of harmonic measure zero. "Twist points" may be ...
    • Graphs of polyhedra; polyhedra as graphs 

      Grünbaum, Branko (2005)
      Relations between graph theory and polyhedra are presented in two contexts. In the first, the symbiotic dependence between 3-connected planar graphs and convex polyhedra is described in detail. In the second, a theory of ...
    • The Heat Equation and Reflected Brownian Motion in Time-Dependent Domains 

      Burdzy, Krzysztof; Chen, Zhen-Qing; Sylvester, John (Institute of Mathematical Statistics, 2004-01)
      The paper is concerned with reflecting Brownian motion (RBM) in domains with deterministic moving boundaries, also known as "non-cylindrical domains," and its connections with partial differential equations. Construction ...
    • The heat equation in time dependent domains with insulated boundaries 

      Burdzy, Krzysztof; Chen, Zhen-Qing; Sylvester, John (Academic Press (Elsevier), 2004-10)
      The paper studies, among other things, two types of possible singularities of the solution to the heat equation at the boundary of a moving domain. Several explicit results on "heat atoms" and "heat singularities" are given.
    • Hitting a boundary point with reflected Brownian motion 

      Burdzy, Krzysztof; Marshall, Donald E. (Springer-Verlag, 1992)
      An explicit integral test involving the reflection angle is given for the reflected Brownian motion in a half-plane to hit a fixed boundary point.
    • Homotopical Topos Theory 

      Warner, Garth (2012-05)
      The purpose of this book is two-fold: (1) To give a systematic introduction to topos theory from a purely categorical point of view, thus ignoring all logical and algebraic issues. (2) To give an account of the homotopy ...
    • The "hot spots" problem in planar domains with one hole. 

      Burdzy, Krzysztof (Duke University Press, 2005)
      There exists a planar domain with piecewise smooth boundary and one hole such that the second eigenfunction for the Laplacian with Neumann boundary conditions attains its maximum and minimum inside the domain.
    • Hölder domains and the boundary Harnack principle 

      Banuelos, Rodrigo; Bass, Richard F.; Burdzy, Krzysztof (Duke University Press, 1991-10)
      A version of the boundary Harnack principle is proven.
    • Intersection local time for points of infinite multiplicity 

      Burdzy, Krzysztof; Bass, Richard F.; Khoshnevisan, Davar (Institute of Mathematical Statistics, 1994-04)
      For each a [is an element of the set] (0, 1/2), there exists a random measure [beta] [subscript] a which is supported on the set of points where two-dimensional Brownian motion spends a units of local time. The measure ...
    • Isogonal prismatoids 

      Grünbaum, Branko (Springer New York, 1997)
      A prismatoid is a polyhedron with all vertices in two parallel planes. A polyhedron P is isogonal if all its vertices form one transitivity class under isometric symmetries of P. Although these restrictions appear very ...