Browsing Mathematics, Department of by Title
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Positivity of Brownian transition densities
(Electronic Journal of Probability, 19970924)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 ... 
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 ... 
Reconstruction Theory
(201101)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 operatorsthen ... 
Reduction of dimensionality in a diffusion search process and kinetics of gene expression
(NorthHolland (Elsevier), 20000301)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 ... 
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 ... 
Sets avoided by Brownian motion
(Institute of Mathematical Statistics, 199804)A fixed twodimensional projection of a threedimensional Brownian motion is almost surely neighborhood recurrent; is this simultaneously true of all the twodimensional projections with probability one? Equivalently: ... 
Shocks and business cycles
(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 ... 
Shocks and Business Cycles
(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 ... 
Shy Couplings
(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 ... 
A Skorobodtype lemma and a decomposition of reflected Brownian motion
(Institute of Mathematical Statistics, 199504)We consider twodimensional 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 ... 
Small trianglefree configurations of points and lines
(2006)In this paper we show that all combinatorial trianglefree 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) trianglefree ... 
Some path properties of iterated Brownian motion
(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 ... 
Stable processes have thorns
(Institute of Mathematical Statistics, 200301)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 ... 
Stochastic bifurcation models
(Institute of Mathematical Statistics, 199901)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 RayKnight theorems), and on time and ... 
Stochastic differential equations driven by stable processes for which pathwise uniqueness fails
(NorthHolland (Elsevier), 200405)Let Z [subscript] t be a onedimensional 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] ... 
SuperBrownian motion with reflecting historical paths
(SpringerVerlag GmbH, 200112)We consider superBrownian motion whose historical paths reflect from each other, unlike those of the usual historical superBrownian motion. We prove tightness for the family of distributions corresponding to a sequence ... 
SuperBrownian motion with reflecting historical paths. II: Convergence of approximations
(SpringerVerlag GmbH, 200510)We prove that the sequence of finite reflecting branching Brownian motion forests defined by Burdzy and Le Gall ([?]) converges in probability to the "superBrownian motion with reflecting historical paths." This solves ... 
The supremum of Brownian local times on Holder curves
(Elsevier, 200111)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 ... 
Synchronous couplings of reflected Brownian motions in smooth domains
(2005)For every bounded planar domain D with a smooth boundary, we define a "Lyapunov exponent" [Lambda](D) using a fairly explicit formula. We consider two reflected Brownian motions in D, driven by the same Brownian motion ... 
A threedimensional Brownian path reflected on a Brownian path is a free Brownian path
(Springer Science+Business Media B.V., 1993)Threedimensional Brownian path reflected on Brownian path is a free Brownian path.