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作者：SHIEH, NR
摘要：We show that certain d-dimensional Markov processes X(t), t greater-than-or-equal-to 0, have the property that if E is a closed subset of R+ with sufficiently large Hausdorff dimension, then X(E) has k-multiple points. This is applied directly to diffusions driven by stochastic differential equations and Levy processes with positive lower indices, solving problems posed by J. P. Kahane and S. J. Taylor.
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作者：LALLEY, SP
摘要：It is proved that if a rational mapping has infinity as a fixed point in its Fatou set, then its Julia set has positive capacity and the equilibrium measure is invariant. If infinity is attracting or superattracting, then the equilibrium measure is strongly mixing, whereas if infinity is neutral, then the equilibrium measure is ergodic and has entropy zero. Lower bounds for the entropy are given in the attracting and superattracting cases. If the Julia set is totally disconnected, then the equ...
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作者：LYONS, R
作者单位：Stanford University
摘要：A collection of several different probabilistic processes involving trees is shown to have an unexpected unity. This makes possible a fruitful interplay of these probabilistic processes. The processes are allowed to have arbitrary parameters and the trees are allowed to be arbitrary as well. Our work has five specific aims: First, an exact correspondence between random walks and percolation on trees is proved, extending and sharpening previous work of the author. This is achieved by establishi...
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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) ...
