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作者：Bruss, FT
作者单位：Universite Libre de Bruxelles; Universite Libre de Bruxelles
摘要：The odds theorem gives a unified answer to a class of stopping problems on sequences of independent indicator functions. The success probability of the optimal rule is known to be larger than Re-R, where R defined in the theorem satisfies R greater than or equal to 1 in the more interesting case. The following findings strengthen this result by showing that 1/e is then a lower bound. Knowing that this is the best possible uniform lower bound motivates this addendum.
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作者：Mairesse, J; Prabhakar, B
作者单位：Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); Stanford University; Stanford University
摘要：A celebrated theorem of Burke's asserts that the Poisson process is a fixed point for a stable exponential single server queue; that is, when the arrival process is Poisson, the equilibrium departure process is Poisson of the same rate. This paper considers the following question: Do fixed points exist for queues which dispense i.i.d. services of finite mean, but otherwise of arbitrary distribution (i.e., the so-called (.)/GI/1/infinity/FCFS queues)? We show that if the service time S is nonco...
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作者：Prabhakar, B
作者单位：Stanford University; Stanford University
摘要：We consider an infinite tandem of first-come-first-served queues. The service times have unit mean, and are independent and identically distributed across queues and customers. Let I be a stationary and ergodic interarrival sequence with marginals of mean tau > 1, and suppose it is independent of all service times. The process I is said to be a fixed point for the first, and hence for each, queue if the corresponding interdeparture sequence is distributed as I. Assuming that such a fixed point...
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作者：Alabert, A; Ferrante, M
作者单位：Autonomous University of Barcelona; University of Padua
摘要：We consider linear nth order stochastic differential equations on [0, 1], with linear boundary conditions supported by a finite subset of [0, 1]. We study some features of the solution to these problems, and especially its conditional independence properties of Markovian type.
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作者：Owhadi, H
作者单位：Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS)
摘要：This paper is concerned with the asymptotic behavior of solutions of stochastic differential equations dy(t) = domega(t) - delV(y(t))dt, y(0) = 0. When d = 1 and V is not periodic but obtained as a superposition of an infinite number of periodic potentials with geometrically increasing periods [V(x) = Sigma(k=0)(infinity) U-k(x/R-k), where U-k are smooth functions of period 1, U-k(0) = 0, and R-k grows exponentially fast with k] we can show that yt has an anomalous slow behavior and we obtain ...
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作者：Jing, BY; Shao, QM; Wang, QY
作者单位：Hong Kong University of Science & Technology; University of Oregon; National University of Singapore; National University of Singapore; University of Sydney
摘要：Let X-1, X-2,... be independent random variables with zero means and finite variances. It is well known that a finite exponential moment assumption is necessary for a Cramer-type large deviation result for the standardized partial sums. In this paper, we show that a Cramer-type large deviation theorem holds for self-normalized sums only under a finite (2 + delta)th moment, 0 < delta less than or equal to 1. In particular, we show P(S-n/ V-n greater than or equal to x) = (1 - Phi(x))(1 + O(1)(1...
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作者：Duan, JQ; Lu, KN; Schmalfuss, B
作者单位：Illinois Institute of Technology; Chinese Academy of Sciences; University of Science & Technology of China, CAS; Brigham Young University; Michigan State University
摘要：Invariant manifolds provide the geometric structures for describing and understanding dynamics of nonlinear systems. The theory of invariant manifolds for both finite- and infinite-dimensional autonomous deterministic systems and for stochastic ordinary differential equations is relatively mature. In this paper, we present a unified theory of invariant manifolds for infinite-dimensional random dynamical systems generated by stochastic partial differential equations. We first introduce a random...
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作者：Karatzas, I; Zikovic, G
作者单位：Columbia University; Columbia University
摘要：We consider the problem of maximizing expected utility from consumption in a constrained incomplete semimartingale market with a random endowment process, and establish a general existence and uniqueness result using techniques from convex duality. The notion of asymptotic elasticity of Kramkov and Schachermayer is extended to the time-dependent case. By imposing no smoothness requirements on the utility function in the temporal argument, we can treat both pure consumption and combined consump...
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作者：Meester, R; Znamenski, D
作者单位：Vrije Universiteit Amsterdam
摘要：One of the key problems related to the Bak-Sneppen evolution model on the circle is computing the limit distribution of the fitness at a fixed observation vertex in the stationary regime as the size of the system tends to infinity. Some simulations have suggested that this limit distribution is uniform on (f, 1) for some f similar to 2/3. In this article, we prove that the mean of the fitness in the stationary regime is bounded away from 1, uniformly in the size of the system, thereby establis...
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作者：Panchenko, D
作者单位：Massachusetts Institute of Technology (MIT)
摘要：We introduce a symmetrization technique that allows us to translate a problem of controlling the deviation of some functionals on a product space from their mean into a problem of controlling the deviation between two independent copies of the functional. As an application we give a new easy proof of Talagrand's concentration inequality for empirical processes, where besides symmetrization we use only Talagrand's concentration inequality on the discrete cube {0, 1}(n). As another application o...
