-
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 ...
-
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...
-
作者：BARLEV, SK; BSHOUTY, D; ENIS, P
作者单位：Technion Israel Institute of Technology; State University of New York (SUNY) System; University at Buffalo, SUNY
摘要：A natural exponential family F is characterized by the pair (V, OMEGA), called the variance function (VF), where OMEGA is the mean domain and V is the variance of F expressed in terms of the mean. Any VF can be used to construct an exponential dispersion model, thus providing a potential generalized linear model. A problem of increasing interest in the literature is the following: Given an open interval OMEGA and a function V defined on OMEGA, is the pair (V, OMEGA) a VF of a natural exponenti...
-
作者：GUTMANN, S; KEMPERMAN, JHB; REEDS, JA; SHEPP, LA
作者单位：AT&T; Nokia Corporation; Nokia Bell Labs; Rutgers University System; Rutgers University New Brunswick
摘要：We show that if f is a probability density on R(n) wrt Lebesgue measure (or any absolutely continuous measure) and 0 less-than-or-equal-to f less-than-or-equal-to 1, then there is another density g with only the values 0 and 1 and with the same (n - 1)-dimensional marginals in any finite number of directions. This sharpens, unifies and extends the results of Lorentz and of Kellerer. Given a pair of independent random variables 0 less-than-or-equal-to X, Y less-than-or-equal-to 1, we further st...
-
作者：CERUTTI, MC; ESCAURIAZA, L; FABES, EB
摘要：We show the well-posedness for the martingale problem associated with a strictly elliptic operator with coefficients bounded and continuous on R(n) except for a countable set having at most one cluster point.
-
作者：ROGERS, LCG; WALSH, JB
作者单位：University of British Columbia
摘要：If (B(t))t greater-than-or-equal-to 0 is Brownian motion on R, if A(t,x) = integral-0t(I){B(s) less-than-or-equal-to x} ds and if tau(.,x) is the right-continuous inverse to A(.,x), then the process BBAR(t,x) = B(tau(t,x)) is a reflecting Brownian motion in (-infinity, x]. If E(x) denotes the sigma-field generated by BBAR(.,x), then (E(x))x-element-of-R forms a filtration. It has been proved recently that all (E(x))-martingales are continuous, in common with the martingales on the Brownian fil...
-
作者：STEIF, JE
摘要：In this paper, we study spin systems, probabilistic cellular automata and interacting particle systems, which are Markov processes with state space {0, 1}Z(n). Restricting ourselves to attractive systems, we consider the stationary processes obtained when either of two distinguished stationary distributions is used, the smallest and largest stationary distributions with respect to a natural partial order on measures. In discrete time, we show that these stationary processes with state space {0...
-
作者：WEINTRAUB, KS
摘要：A random vector is min-stable (or jointly negative exponential) if any weighted minimum of its components has a negative exponential distribution. The vectors can be subordinated to a two-dimensional homogeneous Poisson point process through positive L1 functions called spectral functions. A critical feature of this representation is the point of the Poisson process, called the location, that defines a min-stable random variable. A measure of association between min-stable random variables is ...
-
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...
-
作者：HONG, C; MANDELBAUM, A
作者单位：Stanford University; New Jersey Institute of Technology; Technion Israel Institute of Technology
摘要：Diffusion approximations for stochastic congested networks, both open and closed, are described in terms of the networks' bottlenecks. The approximations arise as limits of functional central limit theorems. The limits are driven by reflected Brownian motions on the nonnegative orthant (for open networks) and on the simplex (for closed ones). The results provide, in particular, invariance principles for Jackson's open queueing networks, Gordon and Newell's closed networks and some of Spitzer's...
