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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：BISHOP, CJ
作者单位：University of California System; University of California Los Angeles
摘要：A planar domain whose boundary E hes in the real line is called a Denjoy domain. In this article we consider some geometric properties of Brownian motion in such a domain. The first result is that if E has zero length (Absolute value of E = 0), then there is a set F subset-of E of full harmonic measure such that every Brownian path which exits at x is-an-element-of F hits both (- infinity, x) and (x, infinity) with probability 1, verifying a conjecture of Burdzy. Next we show that if dim(E) < ...
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作者：LIAO, M
摘要：We prove that if G is a subgroup of the (time-change) symmetry group of a Markov process X(t) which is transitive and has a compact isotropy subgroup, then after a time change, X(t) becomes G-invariant. The symmetry groups of diffusion processes are discussed in more detail. We show that if the generator of X(t) is the Laplacian with respect to the intrinsic metric, then X(t) has the best invariance property.
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作者：KALIKOW, S; WEISS, B
作者单位：Hebrew University of Jerusalem
摘要：Some explicit isomorphisms are constructed between Bernoulli shifts with infinite entropy.
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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：SZCZOTKA, W
摘要：Consider a single-server queue with units served in order of arrival for which we can define a stationary distribution (equilibrium distribution) of the vector of the waiting time and the queue size. Denote this vector by (w(rho), l(rho)), where rho < 1 is the traffic intensity in the system when it is in equilibrium and lambda(rho) is the intensity of the arrival stream to this system. Szczotka has shown under some conditions that (1 - rho)(l(rho) - lambda(rho)w(rho)) --> p 0 as p up 1 (in he...
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作者：MOUNTFORD, TS
摘要：We prove that the critical value for the uniform nearest particle system equals 1.
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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...
