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作者：Zhang, Q.; Yin, G.
作者单位：University System of Georgia; University of Georgia; Wayne State University
摘要：This work is concerned with the asymptotic properties of a singular perturbed nonstationary finite state Markov chain. In a recent paper of the authors, it was shown that as the fluctuation rate of the Markov chain goes to infinity, the probability distribution of the Markov chain converges to its time-dependent quasi-equilibrium distribution. In addition, asymptotic expansion of the probability distribution was obtained. This paper is a continuation of our effort in this direction. Upon using...
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作者：Perman, Mihael; Wellner, Jon A.
作者单位：University of Ljubljana; University of Washington; University of Washington Seattle
摘要：We study the distributions of the areas under the positive parts of a Brownian motion process B and a Brownian bridge process U: with A(+) = integral B-1(0)+ (t) dt and A(0)(+) = integral U-1(0)+ (t) dt, we use excursion theory to show that the Laplace transforms psi(1) (s) = E exp(-sA(1)) and psi(1)(0) (s) = E exp(-sA(0)(+)) of A(+) and A(0)(+) satisfy integral(infinity)(0)e(-lambda s)psi(+)(root 2s(3/2)) ds = lambda(-1/2)Ai(lambda) + (1/3-integral(lambda)(0)Ai(t)dt)/root lambda Ai(lambda)-Ai...
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作者：Bossy, Mireille; Talay, Denis
作者单位：Inria; Universite Cote d'Azur
摘要：In this paper we construct a stochastic particle method for the Burgers equation with a monotone initial condition; we prove that the convergence rate is O (1/root N + root Delta t. for the L-1 (R X Omega). norm of the error. To obtain that result, we link the PDE and the algorithm to a system of weakly interacting stochastic particles; the difficulty of the analysis comes from the discontinuity of the interaction kernel, which is equal to the Heaviside function. In a previous paper we showed ...
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作者：Douglas, Jim, Jr.; Ma, Jin; Protter, Philip
作者单位：Purdue University System; Purdue University
摘要：In this paper we study numerical methods to approximate the adapted solutions to a class of forward-backward stochastic differential equations (FBSDE's). The almost sure uniform convergence as well as the weak convergence of the scheme are proved, and the rate of convergence is proved to be as good as the approximation for the corresponding forward SDE. The idea of the approximation is based on the four step scheme for solving such an FBSDE, developed by Ma, Protter and Yong. For the PDE part,...
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作者：Ethier, S. N.
作者单位：Utah System of Higher Education; University of Utah
摘要：Oscar's system is a gambling system in which the aim is to win one betting unit, at least with high probability, and then start over again. The system can be modeled by an irreducible Markov chain in a subset of the two-dimensional integer lattice. We show that the Markov chain, which depends on a parameter p representing the single-trial win probability, is transient if p < 1/2 and positive recurrent if p >= 1/2
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作者：Fill, James Allen; Mahmoud, Hosam M.; Szpankowski, Wojciech
作者单位：Johns Hopkins University; George Washington University; Purdue University System; Purdue University
摘要：We investigate the duration of an elimination process for identifying a winner by coin tossing or, equivalently, the height of a random incomplete trie. Applications of the process include the election of a leader in a computer network. Using direct probabilistic arguments we obtain exact expressions for the discrete distribution and the moments of the height. Elementary approximation techniques then yield asymptotics for the distribution. We show that no limiting distribution exists, as the a...
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作者：Takacs, Lajos
作者单位：University System of Ohio; Case Western Reserve University
摘要：This paper deals with the distribution function of the sojourn time of Brownian motion with drift. By some recent results of J. Akahori and A. Dassios this distribution function can be expressed in the form of a double integral. In this paper it is shown that the distribution function of the sojourn time can be expressed simply as a single integral. The result obtained is a generalization of the arc-sine law of Paul Levy.
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作者：Berman, Simeon M.
摘要：Let (Xi, Y-i), i = 1, . . . , n, be independent random vectors with a standard bivariate normal distribution and let s(X) and s(Y) be the sample standard deviations. For arbitrary p, 0 < p < 1, define T-i = pX(i) + (1-p)Y-i and Z(i) = pX(i)/s(X) + (1-p)Y-i/s(Y,) i = 1, . . . ,n. The couple of pairs (T-i, Z(i)) and (T-j, Z(j)) is said to be discordant if either T-i < T-j and Z(i) > Z(j) or T-i > T-j and Z(i) < Z(j). It is shown that the expected number of discordant couples of pairs is asymptot...
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作者：Olofsson, Peter
作者单位：Chalmers University of Technology
摘要：A general multitype branching process with sibling dependencies is considered. The dependencies within a group of siblings are described by a joint probability measure, determined by the structure of that particular group. The process is analyzed by means of the embedded macro process, consisting of sibling groups. It is shown that the regular asymptotic behavior of the sibling-dependent process is guaranteed by conditions on the individual reproductions, and that these conditions are exactly ...
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作者：Yao, Yi-Ching; Simons, Gordon
作者单位：Colorado State University System; Colorado State University Fort Collins; Academia Sinica - Taiwan; University of North Carolina; University of North Carolina Chapel Hill
摘要：For an arbitrary point of a homogeneous Poisson point process in a d-dimensional Euclidean space, consider the number of Poisson points that have that given point as their rth nearest neighbor (r = 1, 2, ...). It is shown that as d tends to infinity, these nearest neighbor counts (r = 1, 2, ...) are iid asymptotically Poisson with mean 1. The proof relies on Renyi's characterization of Poisson processes and a representation in the limit of each nearest neighbor count as a sum of countably many...
