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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：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：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：GOROSTIZA, LG; WAKOLBINGER, A
作者单位：Johannes Kepler University Linz
摘要：We consider a system of particles in R(d) performing symmetric stable motion with exponent alpha, 0 < alpha less-than-or-equal-to 2, and branching at the end of an exponential lifetime with offspring generating function F(s) = s + 1/2(1 - s)1+beta, 0 < beta less-than-or-equal-to 1. (This includes binary branching Brownian motion for alpha = 2, beta = 1.) It is shown that, for an initial Poisson population with uniform intensity, the system goes to extinction if d less-than-or-equal-to alpha/be...
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作者：KWAPIEN, S; SZULGA, J
作者单位：Auburn University System; Auburn University
摘要：We prove that if (theta-k) is a sequence of i.i.d. real random variables then, for 1 < q < p, the linear combinations of (theta-k) have comparable pth and qth moments if and only if the joint distribution of (theta-k) is (p, q)-hypercontractive. We elaborate hypercontraction methods in a new proof of the inequality. [GRAPHICS] where (X(i)) is a sequence of independent zero-mean random variables with values in a normed space, and C(p) almost-equal-to p/ln p.
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作者：ADLER, RJ; FELDMAN, RE; LEWIN, M
作者单位：University of California System; University of California Berkeley; University of California System; University of California Santa Barbara
摘要：The Brownian density process is a distribution-valued process that arises either via a limiting operation on an infinite collection of Brownian motions or as the solution of a stochastic partial differential equation. It has a (self-) intersection local time, that is formally defined through an operation involving delta functions, much akin to the better studied intersection local time of measure-valued (super) processes. Our main aim is to show that this formal definition not only makes sense...
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作者：GRIFFIN, P; KUELBS, J
作者单位：University of Wisconsin System; University of Wisconsin Madison
摘要：We study some generalizations of the LIL when self-normalizations are used. Two particular results proved are: (1) an extension of the Kolmogorov-Erdos test for partial sums of symmetric i.i.d. random variables having finite second moments; this result eliminates distinctions required when nonrandom normalizers are used and E(X2I(\X\ > t)) is not O((L2t)-1), and (2) an extension of a universal bounded LIL of Marcinkiewicz to nonsymmetric random variables. An interesting corollary of this work ...
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作者：MAITRA, A; PURVES, R; SUDDERTH, W
作者单位：University of California System; University of California Berkeley
摘要：Starting at x in a Polish space X, a player selects the distribution sigma-0 of the next state x1 from the collection GAMMA(x) of those distributions available and then selects the distribution sigma-1(x1) for x2 from GAMMA(x1) and so on. Suppose the player wins if every x(i) in the stochastic process x1, x2,... lies in a given Borel subset A of X, that is, if the process stays in A forever. If {(x, gamma): gamma epsilon GAMMA(x)} is a Borel subset of X x P(X), where P(X) is the natural Polish...
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作者：HU, IC
摘要：Herein boundary crossing behavior of conditional random walks is studied. Asymptotic distributions of the exit time and the excess over the boundary are derived. In the course of derivation, two results of independent interest are also obtained: Lemma 4.1 shows that a conditional random walk behaves like an unconditional one locally in a very strong sense. Theorem B.1 describes a class of distributions over which the renewal theorem holds uniformly. Applications are given for modified repeated...
