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作者：HILL, TP; KRENGEL, U
摘要：For the secretary (or best-choice) problem with an unknown number N of objects, minimax-optimal stop rules and (worst-case) distributions are derived, under the assumption that N is a random variable with unknown distribution, but known upper bound n. Asymptotically, the probability of selecting the best object in this situation is of order of (log n)-1. For example, even if the only information available is that there are somewhere between 1 and 100 objects, there is still a strategy which wi...
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作者：BEZUIDENHOUT, C; GRIMMETT, G
作者单位：University of Bristol
摘要：We study the contact process, together with a version of the percolation process with one continuously varying coordinate. It is proved here that the radius of the infected cluster has an exponentially decaying tail throughout the subcritical phase. The same is true of the Lebesgue measure (in space-time) of this cluster. Certain critical-exponent inequalities are derived and the critical point of the percolation process in two dimensions is determined exactly.
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作者：ALDOUS, D
摘要：Exact and asymptotic results for the uniform random labelled tree on n vertices have been studied extensively by combinatorialists. Here we treat asymptotics from a modern stochastic process viewpoint. There are three limit processes. One is an infinite discrete tree. The other two are most naturally represented as continuous two-dimensional fractal tree-like subsets of the infinite-dimensional space l1. One is compact; the other is unbounded and self-similar. The proofs are based upon a simpl...
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作者：SHEU, SJ
摘要：In this paper we study the transition density P(t)(x, y) of a nondegenerate diffusion process by using the stochastic control method invented by Fleming and the idea of stochastic parallel translation. We obtain a two-sided estimate for P(t)(x, y) as well as some bounds for the derivatives of log P(t)(x, y).
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作者：DEMBO, A; KARLIN, S
作者单位：Stanford University
摘要：Let (X(i), U(i)) be pairs of i.i.d. bounded real-valued random variables (X(i) and U(i) are generally mutually dependent). Assume E[X(i)] < 0 and Pr{X(i) > 0} > 0. For the (rare) partial sum segments where SIGMA-i = k(l)X(i) --> infinity, strong limit laws are derived for the sums SIGMA-i = k(l)U(i). In particular a strong law for the length (l - k + 1) and the empirical distribution of U(i) in the event of large segmental sums of SIGMA-X(i) are obtained. Applications are given in characterizi...
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作者：KATZENBERGER, GS
摘要：We consider a sequence of R(d)-valued semimartingales {X(n)} satisfying X(n)(t) = X(n)(0) + integral-0/t-sigma-n(X(n)(s-))dZ(n)(s) + integral-0/t(F)(X(n)(s-))DA(n)(s), where {Z(n)} is a well-behaved sequence of R(e)-valued semimartingales, sigma-n is a continuous d x e matrix-valued function, F is a vector field whose deterministic flow has an asymptotically stable manifold of fixed points-GAMMA, and A(n) is a nondecreasing process which asymptotically puts infinite mass on every interval. Man...
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作者：KENNEDY, DP; KERTZ, RP
作者单位：University System of Georgia; Georgia Institute of Technology
摘要：Let X1, X2,... be integrable, i.i.d. r.v.'s with common distribution function F and let {upsilon-n}n greater-than-or-equal-to 1 be the sequence of optimal rewards or values in the associated optimal stopping problem, i.e., upsilon-n = sup{E(X(T)): T is a stopping time for {X(m)}m greater-than-or-equal-to 1 and T less-than-or-equal-to n} for n greater-than-or-equal-to 1. For distribution functions F in the domain of attraction of one of the three classical extreme-value laws G(I), G(II)alpha or...
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作者：DAVIS, RA; RESNICK, SI
作者单位：Cornell University
摘要：Consider moving average processes of the form [GRAPHICS] where {Z(j)} are iid and nonnegative random variables and c(j) > 0 are constants satisfying summability conditions at least sufficient to make the random series above converge. We suppose that the distribution of Z(j) is regularly varying near 0 and discuss lower tail behavior of finite and infinite linear combinations. The behavior is quite different in the two cases. For finite linear combinations, the lower tail is again regularly var...
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作者：AMIT, Y; PICCIONI, M
作者单位：University of Rome Tor Vergata; University of Rome Tor Vergata
摘要：We consider an estimation problem in which the signal is modelled by a continuous Gaussian random field and is observed through smooth and bounded nonlinear sensors. A nonhomogeneous Markov process is defined in order to sample the conditional distribution of the signal given the observations. At any finite time the process takes values in a finite-dimensional space, although the dimension goes to infinity in time. We prove that the empirical averages of any bounded functional continuous w.p.1...
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作者：LINDE, W
摘要：We study the behavior of mu{ is-an-element-of E; parallel-to x parallel-to > t} as t --> infinity for a Gaussian measure mu in a Banach or quasi-Banach space in the following cases: 1. E = l(p), 2 < p < infinity, and mu of diagonal form but not necessarily symmetric; 2. E = Hilbert space and mu-arbitrary; 3. E = l(p)n, 0 < p < 2, and mu of diagonal form. While 2 solves a problem of Hweng (1980), 1 and 3 extend some results of Dobric, Marcus and Weber (1988).
