Browsing Mathematics, Department of by Issue Date
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Lectures on Arrangements
(1974) 
On Brownian Excursions in Lipschitz Domains. Part II: Local Asymptotic Distributions
(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 ... 
Geometric Properties of 2dimensional Brownian Paths
(SpringerVerlag GmbH, 1989)Let A be the set of all points of the plane C, visited by twodimensional 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 ... 
Cut points on Brownian paths
(Institute of Mathematical Statistics, 198907)Let X be a standard twodimensional 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 ... 
Curvature of the convex hull of planar Brownian motion near its minimum point
(NorthHolland (Elsevier), 198910)Let f be a (random) realvalued 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 nonnegative and f(0) = ... 
Nonintersection exponents for Brownian paths. Part I: Existence and an invariance principle
(SpringerVerlag GmbH, 1990)Let X and Y be independent threedimensional 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] ... 
A probabilistic proof of the boundary Harnack principle
(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 ... 
A representation of local time for Lipschitz surfaces
(SpringerVerlag 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 ... 
Percolation dimension of fractals
(Academic Press (Elsevier), 199001)"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 ... 
On nonincrease of Brownian motion
(Institute of Mathematical Statistics, 199007)A new proof of the nonincrease of Brownian paths is given. 
Nonintersection exponents for Brownian paths. Part II: Estimations and applications to a random fractal.
(Institute of Mathematical Statistics, 199007)Let X and Y be independent twodimensional 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 ... 
Minimal Fine Derivatives and Brownian Excursions
(Nagoya University, 199009)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] ... 
A boundary Harnack principle in twisted Hölder domains
(Annals of Mathematics, 199109)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 ... 
Hölder domains and the boundary Harnack principle
(Duke University Press, 199110)A version of the boundary Harnack principle is proven. 
2D Brownian motion in a system of traps: Application of conformal transformations
(Institute of Physics, 1992)We study twodimensional 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 yaxis to the drift ... 
Lifetimes of conditioned diffusions
(SpringerVerlag GmbH, 1992)We investigate when an upper bound on expected lifetimes of conditioned diffusions associated with elliptic operators in divergence and nondivergence form can be found. The critical value of the parameter is found for ... 
Hitting a boundary point with reflected Brownian motion
(SpringerVerlag, 1992)An explicit integral test involving the reflection angle is given for the reflected Brownian motion in a halfplane to hit a fixed boundary point. 
Excursion laws and exceptional points on Brownian paths
(SpringerVerlag, 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. 
The Martin boundary in nonLipschitz domains
(American Mathematical Society, 1993)The Martin boundary with respect to the Laplacian and with respect to uniformly elliptic operators in divergence form can be identified with the Euclidean boundary in C [to the power of gamma] domains, where [gamma](x) = ...