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作者：KALPAZIDOU, S
摘要：Let (S-i, i = 1, 2,..., n), n > 1, be a partition of the circle into sets S-i each consisting of union of delta(i) < infinity, arcs A(kl). Let f(t) be a rotation of length t of the circle and denote Lebesgue measure by lambda. Then every recurrent stochastic matrix P on S = {1,..., n} is given according to a theorem of Cohen (n = 2), Alpern and Kalpazidou (n greater than or equal to 2) by p(ij) = lambda S-i boolean AND f(t)(-1)(S-j))/lambda(Si) for some choice of rotation f(t) and partition L ...
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作者：LeGall, JF; Perkins, EA
作者单位：University of British Columbia
摘要：We show that two-dimensional super-Brownian motion is a multiple of the h-Hausdorff measure on its closed support, where h(r) = r(2) log(+)(1/r)log(+) log(+) log(+) (1/r). This complements known results in dimensions greater than 2.
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作者：Lu, SL
作者单位：University of Michigan System; University of Michigan
摘要：We discuss the hydrodynamic scaling limits starting with deterministic configurations for different models. Certain estimates on the entropy of the system are derived.
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作者：MONAT, P; STRICKER, C
摘要：Let X be an R(d)-valued special semimartingale on a probability space (Omega,F,(F-t)(0 less than or equal to t less than or equal to T), P) with decomposition X = X(0) + M + A and Theta the space of all predictable, X-integrable processes theta such that integral theta dX is in the space P-2 of semimartingales. If H is a random variable in L(2), We prove, under additional assumptions on the process X, that H can be written as the sum of an F-0-measurable random variable H-0, a stochastic integ...
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作者：Lee, TY; Remillard, B
作者单位：University of Quebec; University of Quebec Trois Rivieres
摘要：Let mu(t)(dx) denote a three-dimensional super-Brownian motion with deterministic initial state mu(0)(dx) = dx, the Lebesgue measure. Let V: R(3) --> R be Holder-continuous with compact support, not identically zero and such that integral(R3)V(x) dx = 0. We show that log P {integral(0)(t) integral(R3)V(x)mu(s)(dx)ds > bt(3/4)} is of order t(1/2) as t --> infinity, for b > 0. This should be compared with the known result for the case integral(R3)V(x)dx > 0. In that case the normalization bt(3/4...
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作者：Sudbury, A; Lloyd, P
摘要：Duality has proved to be a powerful tool in the theory of interacting particle systems. The approach in this paper is algebraic rather than via Harris diagrams. A form of duality is found which includes coalescing and annihilating duality as special cases. This enables new results for the branching annihilating random walk and the biased annihilating branching process to be derived.
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作者：DEUSCHEL, JD; ZEITOUNI, O
作者单位：Technion Israel Institute of Technology
摘要：We consider the concentration of measure for n i.i.d., two-dimensional random variables under the conditioning that they form a record. Under mild conditions, we show that all random variables tend to concentrate, as n --> infinity, around Limiting curves, which are the solutions of an appropriate variational problem. We also show that the same phenomenon occurs, without the records conditioning, for the longest increasing subsequence in the sample.
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作者：WANG, G
摘要：Let X and Y be two continuous-time martingales. If quadratic variation of X minus that of Y is a nondecreasing and nonnegative function of time, we say that Y is differentially subordinate to X and prove that \\Y\\(p) less than or equal to (p* - 1)\\X\\(p) for 1 < p < infinity, where p* = p boolean OR q and q is the conjugate of p. This inequality contains Burkholder's L(p)-inequality for stochastic integrals, which implies that the above inequality is sharp. We also extend his concept, of str...
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作者：BASS, RF; KHOSHNEVISAN, D
摘要：We give exact expansions for the upper and lower tails of the distribution of the maximum of local time of standard Brownian bridge on interval [0, 1]. We use the above expansions to prove upper and lower laws of the iterated logarithm for the maximum of the local time of the uniform empirical process. This solves two open problems cited in the book of Shorack and Wellner.
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作者：BENJAMINI, I; PEMANTLE, R; PERES, Y
作者单位：University of Wisconsin System; University of Wisconsin Madison; University of California System; University of California Berkeley
摘要：The probability that a transient Markov chain, or a Brownian path, will ever visit a given set Lambda is classically estimated using the capacity of Lambda with respect to the Green kernel G(x, y). We show that replacing the Green kernel by the Martin kernel G(x, y)/G(0, y) yields improved estimates, which are exact up to a factor of 2. These estimates are applied to random walks on lattices and also to explain a connection found by Lyons between capacity and percolation on trees.
