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作者：Mahmoud, Hosam M.
作者单位：George Washington University
摘要：By embedding in a suitable continuous-time process, we find a strong law for h(n), the height of a random binary pyramid of order n. We show that h(n)/ln n converges almost surely to a constant limit and we determine that limit.
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作者：El Karoui, Nicole; Karatzas, Ioannis
作者单位：Sorbonne Universite; Columbia University
摘要：We present an approach to the general, non-Markovian dynamic allocation (or multiarmed bandit) problem, formulated in continuous time as a problem of stochastic control for multiparameter processes in the manner of Mandelbaum. This approach is based on a direct, martingale study of auxiliary questions in optimal stopping. Using a methodology similar to that of Whittle and relying on simple time-change arguments, we construct Gittins-index-type strategies, verify their optimality, provide expli...
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作者：Alexander, Kenneth S.
作者单位：University of Southern California
摘要：Functionals L on finite subsets A of R'1 are considered for which the value is the minimum total edge length among a class of graphs with vertex set equal to, or in some cases containing, A. Examples include minimal spanning trees, the traveling salesman problem, minimal matching and Steiner trees. Beardwood, Halton and Hammersley, and later Steele, have shown essentially that for {X1,, X,,} a uniform i.i.d. sample from [0,1](d), EL({X-1, . . . , X-n})/n((d-1)/d) converges to a finite constant...
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作者：Arnold, Ludwig; Gundlach, Volker Matthias; Demetrius, Lloyd
作者单位：University of Bremen; Harvard University
摘要：We present a formalism to investigate directionality principles in evolution theory for populations, the dynamics of which can be described by a positive matrix cocycle (product of random positive matrices). For the latter, we establish a random version of the Perron-Frobenius theory which extends all known results and enables us to characterize the equilibrium state of a corresponding abstract symbolic dynamical system by an extremal principle. We develop a thermodynamic formalism for random ...
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作者：Arratia, Richard; Waterman, Michael S.
作者单位：University of Southern California; University of Southern California
摘要：We consider a sequence matching problem involving the optimal alignment score for contiguous subsequences, rewarding matches and penalizing for deletions and mismatches. This score is used by biologists comparing pairs of DNA or protein sequences. We prove that for two sequences of length n, as n -> infinity, there is a phase transition between linear growth in n, when the penalty parameters are small, and logarithmic growth in n, when the penalties are large. The results are valid for indepen...
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作者：Athreya, K. B.
作者单位：Iowa State University
摘要：Let {Z(n)}(0)(infinity) be a Galton-Watson branching process with offspring distribution {p(j)}(0)(infinity). We assume throughout that p(0) = 0, pj = 0, p(j) not equal 1 for any j >= 1 and 1 < m = Sigma jp(j) < infinity. Let W-n = Z(n) m (-n) and W-n = lim(n) W-n. In this paper we study the rates of convergence to zero as n -> infinity of P( vertical bar Z(n+1)/z(n) - m vertical bar > epsilon), P(vertical bar W-n - W vertical bar > epsilon), P( vertical bar Z(n+1)/z(n) - m vertical bar > epsi...
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作者：Dupuis, Paul; Oliensis, John
作者单位：Brown University; University of Massachusetts System; University of Massachusetts Amherst
摘要：The main problem considered in this paper is the construction of numerical methods and proofs of their convergence for the problem of shape from shading. In the first part of the paper, it is assumed that the height function that describes the surface to be reconstructed is known at all local minima (or maxima). These points are a subset of the singular points, which are the brightest points in the image. A pair of optimal control problems are defined that provide representations for the heigh...
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作者：Finnoff, William
作者单位：Siemens AG; Siemens Germany
摘要：A model for the activities of a finite number of agents in an economy is presented as the solution to a system of stochastic differential equations driven by general semimartingales and displaying an extended form of strong local interaction. We demonstrate a law of large numbers for the systems of processes as the number of agents goes to infinity under a weak convergence hypothesis on the triangular array of starting values and driving semimartingales which induces the systems of equations. ...
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作者：Perfekt, Roland
作者单位：Lund University
摘要：In this paper the extremal behaviour of real-valued, stationary Markov chains is studied under fairly general assumptions. Conditions are obtained for convergence in distribution of multilevel exceedance point processes associated with suitable families of high levels. Although applicable to general stationary sequences, these conditions are tailored for Markov chains and are seen to hold for a large class of chains. The extra assumptions used are that the marginal distributions belong to the ...
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作者：Fricker, Christine; Robert, Philippe; Saada, Ellen; Tibi, Danielle
作者单位：Inria; Centre National de la Recherche Scientifique (CNRS); Universite de Rouen Normandie; Universite Paris Cite
摘要：In this paper we study a stochastic network model introduced recently in the analysis of neural networks. In this model the interaction between the nodes of the network is local: with each node is associated some real number (the inhibition in the language of neural networks) which is decreasing linearly with time. When this number reaches 0, it sends out some random input to its neighbors (a spike) and restarts with some random value. The state of our network is described as a Markov process....
