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作者：DALANG, RC; WALSH, JB
作者单位：University of British Columbia
摘要：This paper examines the question of when a two-parameter process X of independent increments will have Levy's sharp Markov property relative to a given domain D. This property states intuitively that the values of the process inside D and outside D are conditionally independent given the values of the process on the boundary of D. Under mild assumptions, X is the sum of a continuous Gaussian process and an independent jump process. We show that if X satisfies Levy's sharp Markov property, so d...
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作者：SCHINAZI, R
摘要：We apply an invariance principle due to De Masi, Ferrari, Goldstein and Wick to the edge process for critical reversible nearest-particle systems. Their result also gives an upper bound for the diffusion constant that we compute explicitly. A comparison between the movement of the edge, when the other particles are frozen, and a random walk allows us to find a lower bound for the diffusion constant. This shows that the right renormalization for the edge to converge to a nondegenerate Brownian ...
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作者：NOLAN, JP
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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...
