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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：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：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：Resnick, Sidney I.; Roy, Rishin
作者单位：Cornell University; University of Toronto
摘要：A general framework in an ordinal utility setting for the analysis of dynamic choice from a continuum of alternatives E is proposed. The model is based on the theory of random utility maximization in continuous time. We work with superextremal processes Y = {Y-t, t is an element of (0, infinity)}, where Y-t = {Y-t(tau), tau is an element of E} is a random element of the space of upper semicontinuous functions on a compact metric space E. Here Y-t(tau) represents the utility at time t for alter...
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作者：Shreve, S. E.; Soner, H. M.
作者单位：Carnegie Mellon University
摘要：A complete solution is provided to the infinite-horizon, discounted problem of optimal consumption and investment in a market with one stock, one money market (sometimes called a bond) and proportional transaction costs. The utility function may be of the form c(p)/p, where p < 0 or 0 < p < 1, or may be log c. It is assumed that the interest rate for the money market is positive, the mean rate of return for the stock is larger than this interest rate, the stock volatility is positive and all t...
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作者：Frieze, Alan; Kannan, Ravi; Polson, Nick
作者单位：Carnegie Mellon University; Telcordia Technologies; Carnegie Mellon University; University of Chicago
摘要：We consider the problem of sampling according to a distribution with log-concave density F over a convex body K subset of R-n. The sampling is dine using a biased random walk, and polynomial upper bounds on the time to get a sample point with disribution close to F.
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作者：Bramson, Maury
作者单位：University of Wisconsin System; University of Wisconsin Madison
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作者：Sigman, Karl; Yao, David D.
作者单位：Columbia University
摘要：We study a continuous time inventory process that is a reflection mapping of a semimartingale netput process. Inventory processes of this type include the workload process in queues, dam and storage processes (with perhaps pure jump Levy input), as well as processes arising in fluid models. We establish sufficient conditions on the netput ensuring that the steady-state inventory has finite moments of order k 1, and derive explicit bounds for these moments. The sufficient conditions require tha...
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作者：Bramson, Maury
作者单位：University of Wisconsin System; University of Wisconsin Madison
摘要：A class of open first-in, first-out queueing networks is examined. Customers arrive according to a rate-1 Poisson process and wait at queues along their prescribed routes for exponential holding times, after which they exit from the system. Such a network can be chosen so that the sum of the mean service times at each queue is as small as desired. It is shown here that these networks are nevertheless unstable. Each such network will possess two customer types, which proceed along nearly parall...
