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作者：ASMUSSEN, S
摘要：The distributions of random walk quantities like ascending ladder heights and the maximum are shown to be phase-type provided that the generic random walk increment X has difference structure X = U - T with U phase-type, or the one-sided assumption of X+ being phase-type is imposed. As a corollary, it follows that the stationary waiting time in a GI/PH/1 queue with phase-type service times is again phase-type. The phase-type representations are characterized in terms of the intensity matrix Q ...
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作者：PEDDADA, SD
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作者：BERTOIN, J; LEJAN, Y
摘要：Let X be a Hunt process starting from a regular recurrent point 0 and nu a smooth probability measure on the state space. We show that T = inf{s: A(s) > L(s)}, where A is the continuous additive functional associated to nu and L the local time at 0, solves the Skorokhod problem for nu, that is, X(T) has law-nu. We construct another solution which minimizes E0(B(S)) among all the solutions S of the Skorokhod problem, where B is any positive continuous additive functional. The special case where...
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作者：JUREK, ZJ
作者单位：University of Wroclaw
摘要：A notion of U-exponents of a probability measure on a linear space is introduced. These are bounded linear operators and it is shown that the set of all U-exponents forms a Lie wedge for full measures on finite-dimensional spaces. This allows the construction of U-exponents commuting with the symmetry group of a measure in question. Then the set of all commuting exponents is described and elliptically symmetric measures are characterized in terms of their Fourier transforms. Also, self-decompo...
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作者：BASAK, GK; BHATTACHARYA, RN
作者单位：Indiana University System; Indiana University Bloomington
摘要：A verifiable criterion is derived for the stability in distribution of singular diffusions, that is, for the weak convergence of the transition probability p(t; x, dy), as t --> infinity, to a unique invariant probability. For this we establish the following: (i) tightness of {p(t; x, dy): t greater-than-or-equal-to 0}; and (ii) asymptotic flatness of the stochastic flow. When specialized to highly nonradial nonsingular diffusions the results here are often applicable where Has'minskii's well-...
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作者：LYONS, R; PEMANTLE, R
作者单位：University of Wisconsin System; University of Wisconsin Madison; Stanford University; University of California System; University of California Berkeley
摘要：We show that the transience or recurrence of a random walk in certain random environments on an arbitrary infinite locally finite tree is determined by the branching number of the tree, which is a measure of the average number of branches per vertex. This generalizes and unifies previous work of the authors. It also shows that the point of phase transition for edge-reinforced random walk is likewise determined by the branching number of the tree. Finally, we show that the branching number dete...
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作者：DINWOODIE, IH; ZABELL, SL
摘要：Say that a family (P(theta)n: theta is-an-element-of THETA) of sequences of probability measures is exponentially continuous if whenever theta(n) --> theta, the sequence {P(theta-n)n} satisfies a large deviation principle with rate function lambda(theta). If THETA is compact and {P(theta)n} is exponentially continuous, then the mixture P(n)(A) =: integral-THETA P(theta)n(A)d-mu(theta) satisfies a large deviation principle with rate function lambda(x) =: inf{lambda(theta)(x): theta is-an-elemen...
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作者：FREIDLIN, MI; WENTZELL, AD
作者单位：Lomonosov Moscow State University
摘要：We consider semilinear parabolic PDE's with fast oscillating boundary conditions. The central limit theorem and limit theorems for probabilities of large deviations for the solutions of such problems are proved.
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作者：MELFI, VF
作者单位：University of Michigan System; University of Michigan
摘要：An analogue of the Lai-Siegmund nonlinear renewal theorem is proved for processes of the form S(n) + xi(n), where {S(n)} is a Markov random walk. Specifically, Y0, Y1,... is a Markov chain with complete separable metric state space; X1, X2,... is a sequence of random variables such that the distribution of X(i) given {Y(j), j greater-than-or-equal-to 0} and {X(j), j not-equal i} depends only on Y(i-1) and Y(i); S(n) = X1 + ... +X(n); and {xi(n)} is slowly changing, in a sense to be made precis...
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作者：ALEXANDER, KS; KALIKOW, SA
摘要：Given a finite alphabet, there is an inductive method for constructing a stationary measure on doubly infinite words from this alphabet. This construction can be randomized; the main focus here is on a particular uniform randomization which intuitively corresponds to the idea of choosing a generic stationary process. It is shown that with probability 1, the random stationary process has zero entropy and gives positive probability to every periodic infinite word.
