ResearchWorks Archive

Browsing Mathematics, Department of by Issue Date

Browsing Mathematics, Department of by Issue Date

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  • Klee, Victor (1960)
  • Grünbaum, Branko (1974)
  • Burdzy, Krzysztof; Toby, Ellen H.; Williams, Ruth J. (Birkhäuser Boston, Inc., 1989)
    In this paper, we continue the study initiated in Burdzy and Williams (1986) of the local properties of Brownian excursions in Lipschitz domains. The focus in part I was on local path properties of such excursions. In ...
  • 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 ...
  • Burdzy, Krzysztof (Institute of Mathematical Statistics, 1989-07)
    Let X be a standard two-dimensional Brownian motion. There exists a.s. t [is an element of the set] (0; 1) such that X([0; t))[intersected with] X((t; 1]) = [empty set]. It follows that X([0; 1]) is not homeomorphic to ...
  • Burdzy, Krzysztof; San Martin, Jaime (North-Holland (Elsevier), 1989-10)
    Let f be a (random) real-valued function whose graph represents the boundary of the convex hull of planar Brownian motion run until time 1 near its lowest point in a coordinate system so that f is non-negative and f(0) = ...
  • Burdzy, Krzysztof; Bass, Richard F. (Birkhauser Boston, Inc., 1990)
    The main purpose of this paper is to give a probabilistic proof of Theorem 1.1, one using elementary properties of Brownian motion. We also obtain the fact that the Martin boundary equals the Euclidean boundary as an easy ...
  • Burdzy, Krzysztof; Lawler, Gregory F. (Springer-Verlag GmbH, 1990)
    Let X and Y be independent three-dimensional Brownian motions, X(0) = (0; 0; 0), Y (0) = (1; 0; 0) and let p [subscript]r = P(X[0; r] [intersected with] Y [0; r] = [empty set]. Then the "non- intersection exponent" [from] ...
  • Banuelos, Rodrigo; Bass, Richard F.; Burdzy, Krzysztof (Springer-Verlag GmbH, 1990)
    Suppose that D [is an element of the set of Real numbers to the power of n], n [is greater than or equal to] 2, is a Lipschitz domain and let N[subscript]t(r) be the number of excursions of Brownian motion inside D with ...
  • Burdzy, Krzysztof (Academic Press (Elsevier), 1990-01)
    "Percolation dimension" is introduced in this note. It characterizes certain fractals and its definition is based on the Hausdorff dimension. It is shown that percolation dimension and "boundary dimension" are in a sense ...
  • Burdzy, Krzysztof; Lawler, Gregory F. (Institute of Mathematical Statistics, 1990-07)
    Let X and Y be independent two-dimensional Brownian motions, X(0) = (0; 0); Y(0) = ([epsilon]; 0), and let p([epsilon]) = P(X[0; 1] [intersected with] Y [0; 1] = [empty set], q([epsilon]) = {Y [0; 1] does not contain a ...
  • Burdzy, Krzysztof (Institute of Mathematical Statistics, 1990-07)
    A new proof of the non-increase of Brownian paths is given.
  • Burdzy, Krzysztof (Nagoya University, 1990-09)
    Let f be an analytic function defined on D [is a subset of] [complex numbers] C. If [the derivative of the function f at the point x] has a limit when [the set] x [into the set] z [is an element of the set partial derivative] ...
  • Burdzy, Krzysztof; Bass, Richard F. (Annals of Mathematics, 1991-09)
    The boundary Harnack principle for the ratio of positive harmonic functions is shown to hold in twisted Hölder domains of order [alpha] for [alpha is an element of the set](1/2, 1]. For each [alpha is an element of the ...
  • Banuelos, Rodrigo; Bass, Richard F.; Burdzy, Krzysztof (Duke University Press, 1991-10)
    A version of the boundary Harnack principle is proven.
  • Burdzy, Krzysztof; Bass, Richard F. (Springer-Verlag GmbH, 1992)
    We investigate when an upper bound on expected lifetimes of conditioned diffusions associated with elliptic operators in divergence and non-divergence form can be found. The critical value of the parameter is found for ...
  • 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.
  • Burdzy, Krzysztof; Holyst, Robert; Salisbury, Thomas S. (Institute of Physics, 1992)
    We study two-dimensional Brownian motion in a periodic system of traps using conformal transformations. The system is periodic in the x and y directions. We calculate the ratio of the drift along the y-axis to the drift ...
  • Burdzy, Krzysztof (Birkhauser Boston, Inc., 1993)
    The present paper is devoted to studying path properties of iterated Brownian motion (IBM). We want to examine how the lack of independence of increments influences the results and estimates which are well understood in ...
  • Burdzy, Krzysztof; Marshall, Donald E. (Elsevier, 1993)
    Our main results are (i) a new construction of reflected Brownian motion X in a half-plane with non-smooth angle of oblique reflection and (ii) a theorem on existence of some "exceptional" points on the paths of the ...

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