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作者：LALLEY, S; SELLKE, T
摘要：Let R(t) be the position of the rightmost particle at time t in a time-homogeneous one-dimensional branching diffusion process. Let gamma(alpha, t) be the alpha-th quantile of R(t) under P0, where P(x) denotes the probability measure of the branching diffusion process starting with a single particle at position x. We show that gamma(alpha, t) is a limiting quantile of R(t) under P(x) in the sense that lim(t-->infinity) P(x){R(t) less-than-or-equal-to gamma(alpha, t)} exists for all alpha is-an...
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作者：GILAT, D; HILL, TP
作者单位：University System of Georgia; Georgia Institute of Technology
摘要：A one-sided refinement of the strong law of large numbers is found for which the partial weighted sums not only converge almost surely to the expected value, but also the convergence is such that eventually the partial sums all exceed the expected value. The new weights are distribution-free, depending only on the relative ranks of the observations. A similar refinement of the Glivenko-Cantelli theorem is obtained, in which a new empirical distribution function not only has the usual uniformly...
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作者：WOOD, GR
摘要：We answer two questions: What is the probability that a randomly chosen distribution function on {0, 1,..., n} is a mixture of binomial distributions? and What is the probability that an n-exchangeable sequence is the initial segment of an infinite exchangeable sequence? Curiously, the answers are the same.
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作者：BARBOUR, AD; BROWN, TC
作者单位：University of Western Australia
摘要：The paper gives bounds for the accuracy of Poisson approximation to the distribution of the number of points in a point process. There are two principal bounds, one in terms of reduced Palm probabilities for general point processes, and one involving compensators for point processes on the fine. The latter bound is frequently sharper than the previously used compensator bounds when the expected number of points is large, and examples show that little improvement is possible without changing th...
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作者：FERNIQUE, X
摘要：In this note, we study the regularity of R(N)-valued random functions X = (X(n), n is-an-element-of N) on R such that X(n)(t) = a(n)x(n)(b(n)t), t is-an-element-of R, n is-an-element-of N, where a = (a(n)) subset-of R+, b = (b(n)) subset-of R+ and (X(n), n is-an-element-of N) is an i.i.d. sequence of gaussian centered stationary real random functions on R. If the common covariance of the x(n)'s verifies some very weak regularity assumptions, then their paths are continuous in l(p), p is-an-ele...
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作者：BRASSESCO, S
摘要：The joint density of the total winding and the radius of a planar Brownian motion is calculated, by solving the associated backward equation. An explicit expression for the distribution of the hitting time of an angular barrier is shown; in particular, the behavior of the tail of the distribution is determined.
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作者：DEHEUVELS, P; MASON, DM
作者单位：University of Delaware
摘要：Let {alpha(n)(t), 0 less-than-or-equal-to t less-than-or-equal-to 1} and {beta(n)(t), 0 less-than-or-equal-to t less-than-or-equal-to 1} be the empirical and quantile processes generated by the first n observations from an i.i.d. sequence of uniformly distributed random variables on (0, 1). Let 0 < alpha(n) < 1 be a sequence of constants such that alpha(n) --> 0 as n --> infinity. We investigate the strong limiting behavior as n --> infinity of the increment functions {alpha(n)(t + alpha(n)s) ...
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作者：HILDEBRAND, A
摘要：Let X(n), n greater-than-or-equal-to 1, be a sequence of independent random variables, and let F(N) be the distribution function of the partial sums SIGMA(n = 1)N X(n). Motivated by a conjecture of Erdos in probabilistic number theory, we investigate conditions under which the convergence of F(N)(x) at two points x = x1, x2 with different limit values already implies the weak convergence of the distributions F(N). We show that this is the case if SIGMA(n = 1)infinity rho(X(n), c(n)) = infinity...
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作者：SAMUELCAHN, E
摘要：Let X(i) be i.i.d. random variables, 0 less-than-or-equal-to X(i) less-than-or-equal-to 1 and c greater-than-or-equal-to 0, and let Y(i) = X(i) - ic. It is shown that for all n, all c and all such X(i), E(max(i greater-than-or-equal-to 1 Y(i)) - sup(t) EY(t) < e-1, where t is a stopping rule and e-1 is shown to be the best bound for which the inequality holds. Specific bounds are also obtained for fixed n or fixed c. These results are very similar to those obtained by Jones for a similar probl...
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作者：THOMASSEN, C
摘要：The two-dimensional grid Z2 and any graph of smaller growth rate is recurrent. We show that any graph satisfying an isoperimetric inequality only slightly stronger than that of Z2 is transient. More precisely, if f(k) denotes the smallest number of vertices in the boundary of a connected subgraph with k vertices, then the graph is transient if the infinite sum SIGMA-f(k)-2 converges. This can be applied to parabolicity versus hyperbolicity of surfaces.
