ResearchWorks Archive

Browsing EPrint Collection - Mathematics by Title

Browsing EPrint Collection - Mathematics by Title

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  • 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 ...
  • Warner, Garth (2009-12-23)
    These notes provide a systematic account of certain aspects of the statistical structure of quantum theory. Here the all prevailing notion is that of a completely positive map and Stinespring's famous characterization ...
  • Burdzy, Krzysztof; Barlow, Martin T.; Bass, Richard F. (Electronic Journal of Probability, 1997-09-24)
    Let B be a Borel subset of R [to the power of] d and let p(t, x, y) be the transition densities of Brownian motion killed on leaving B. Fix x and y in B. If p(t, x, y) is positive for one t, it is positive for every value ...
  • 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 ...
  • Warner, Garth (2011-01)
    Suppose that G is a compact group. Denote by \underline{Rep} G the category whose objects are the continuous finite dimensional unitary representations of G and whose morphisms are the intertwining operators--then ...
  • Burdzy, Krzysztof; Holyst, Robert; Blazejezyk, M.; Goralski, G.; Bocquet, L. (North-Holland (Elsevier), 2000-03-01)
    In order to activate a gene in a DNA molecule a specific protein (transcription factor) has to bind to the promoter of the gene. We formulate and partially answer the following question: how much time does a transcription ...
  • 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; Adelman, Omer; Pemantle, Robin (Institute of Mathematical Statistics, 1998-04)
    A fixed two-dimensional projection of a three-dimensional Brownian motion is almost surely neighborhood recurrent; is this simultaneously true of all the two-dimensional projections with probability one? Equivalently: ...
  • Burdzy, Krzysztof; Frankel, David M. (Berkeley Electronic Press, 2005)
    A popular theory of business cycles is that they are driven by animal spirits: shifts in expectations brought on by sunspots. A prominent example is Howitt and McAfee (AER, 1992). We show that this model has a unique ...
  • Frankel, David M.; Burdzy, Krzysztof (2005)
    A popular theory of business cycles is that they are driven by animal spirits: shifts in expectations brought on by sunspots. A prominent example is Howitt and McAfee (AER, 1992). We show that this model has a unique ...
  • Benjamini, Itai; Burdzy, Krzysztof; Chen, Zhen-Qing (2005)
    A pair (X; Y) of Markov processes is called a Markov coupling if X and Y have the same transition probabilities and (X;Y) is a Markov process. We say that a coupling is "shy" if there exists a (random) [Epsilon] > 0 such ...
  • Burdzy, Krzysztof; Toby, Ellen H. (Institute of Mathematical Statistics, 1995-04)
    We consider two-dimensional reflected Brownian motions in sharp thorns pointed downward with horizontal vectors of reflection. We present a decomposition of the process into a Brownian motion and a process which has bounded ...
  • Boben, Marko; Grünbaum, Branko; Pisanski, Tomaz; Zitnik, Arjana (2006)
    In this paper we show that all combinatorial triangle-free configurations (v_3) for v (is less than or equal to) 8 are geometrically realizable. We also show that there is a unique smallest astral (18_3) triangle-free ...
  • 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; Kulczycki, Tadeusz (Institute of Mathematical Statistics, 2003-01)
    Let X(t) be the symmetric [alpha]-stable process in R [to the power of] d, [alpha is an element of the set] (0, 2), d [is greater than or equal to] 2. For f : (0, 1) [approaching] (0,[infinity]) let D(f) be the thorn {x ...
  • Burdzy, Krzysztof; Bass, Richard F. (Institute of Mathematical Statistics, 1999-01)
    We study an ordinary differential equation controlled by a stochastic process. We present results on existence and uniqueness of solutions, on associated local times (Trotter and Ray-Knight theorems), and on time and ...
  • Burdzy, Krzysztof; Bass, Richard F.; Chen, Zhen-Qing (North-Holland (Elsevier), 2004-05)
    Let Z [subscript] t be a one-dimensional symmetric stable process of order [alpha] with [alpha is an element of the set] (0, 2) and consider the stochastic differential equation dX [subscript] t = [omega] (X [subscript] ...
  • Burdzy, Krzysztof; Le Gall, Jean-Francois (Springer-Verlag GmbH, 2001-12)
    We consider super-Brownian motion whose historical paths reflect from each other, unlike those of the usual historical super-Brownian motion. We prove tightness for the family of distributions corresponding to a sequence ...
  • Burdzy, Krzysztof; Mytnik, Leonid (Springer-Verlag GmbH, 2005-10)
    We prove that the sequence of finite reflecting branching Brownian motion forests defined by Burdzy and Le Gall ([?]) converges in probability to the "super-Brownian motion with reflecting historical paths." This solves ...
  • Burdzy, Krzysztof; Bass, Richard F. (Elsevier, 2001-11)
    For f : [maps the set] [0, 1] [into the set of real numbers] R, we consider L ([to the power of] f [subscript] t), the local time of spacetime Brownian motion on the curve f. Let S [subscript alpha] be the class of all ...

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