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作者：Bass, RF; Burdzy, K
作者单位：University of Connecticut; University of Washington; University of Washington Seattle
摘要：We study an ordinary differential equation controlled by a stochastic process. We present results on existence and uniqueness of solutions, on associated local times (Trotter and Ray-Knight theorems) and on time and direction of bifurcation. A relationship with Lipschitz approximations to Brownian paths is also discussed.
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作者：Benjamini, I; Pemantle, R; Peres, Y
作者单位：Weizmann Institute of Science; University of Wisconsin System; University of Wisconsin Madison; Hebrew University of Jerusalem; University of California System; University of California Berkeley
摘要：We construct a nearest-neighbor process {S-n} on Z that is less predictable than simple random walk, in the sense that given the process until time n, the conditional probability that Sn+k = x is uniformly bounded by Ck(-alpha) for some alpha > 1/2. From this process, we obtain a probability measure mu on oriented paths in Z(3) such that the number of intersections of two paths, chosen independently according to mu, has an exponential tail. (For d greater than or equal to 4, the uniform measur...
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作者：Salzano, M; Schonmann, RH
作者单位：University of California System; University of California Los Angeles
摘要：We provide a new proof, substantially simpler than Zhang's original one, that for the contact process on homogeneous trees, local survival implies complete convergence.
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作者：Schechtman, G; Schlumprecht, T; Zinn, J
作者单位：Weizmann Institute of Science; Texas A&M University System; Texas A&M University College Station
摘要：The Gaussian correlation conjecture states that for any two symmetric, convex sets in n-dimensional space and for any centered, Gaussian measure on that space, the measure of the intersection is greater than or equal to the product of the measures. In this paper we obtain several results which substantiate this conjecture. For example, in the standard Gaussian case, we show there is a positive constant, c, such that the conjecture is true if the two sets are in the Euclidean ball of radius c r...
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作者：Lee, TY; Torcaso, F
作者单位：University System of Maryland; University of Maryland College Park
摘要：We extend a result of Freidlin and Gartner for KPP wave fronts to the case d greater than or equal to 2 for i.i.d. random media. We show a wave front propagation speed is attained for the discrete-space (lattice) KPP using a large deviation approach.
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作者：Albin, JMP
作者单位：Chalmers University of Technology; University of Gothenburg
摘要：We derive upper and lower asymptotic bounds for the distribution of the supremum for a self-similar stochastic process. As an intermediate step, most proofs relate suprema to sojourns before proceeding to an appropriate discrete approximation. Our results rely on one or more of three assumptions, which in turn essentially require weak convergence, existence of a first moment and tightness, respectively. When all three assumptions hold, the upper and lower bounds coincide (Corollary 1). For P-s...
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作者：Mountford, T; Sweet, T
作者单位：University of California System; University of California Los Angeles
摘要：Approximating a critical attractive reversible nearest particle system on a finite set from above is not difficult, but approximating it from below is less trivial, as the empty configuration is invariant. We develop a finite state Markov chain that deals with this issue. The rate of convergence for this chain is discovered through a mixing inequality in Jerrum and Sinclair; an application of that spectral gap bound in this case requires the use of randomized paths from state to state. For app...
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作者：Seppalainen, T
作者单位：Iowa State University
摘要：We derive the limiting shape for the following model of first-passage bond percolation on the two-dimensional integer lattice: the percolation is directed in the sense that admissible paths are nondecreasing in both coordinate directions. The passage times of horizontal bonds are Bernoulli distributed, while the passage times of vertical bonds are all equal to a deterministic constant. To analyze the percolation model, we couple it with a one-dimensional interacting particle system. This parti...
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作者：Cvitanic, J; Karatzas, I; Soner, HM
作者单位：Columbia University; Columbia University; Bogazici University
摘要：We consider backward stochastic differential equations with convex constraints on the gains (or intensity-of-noise) process. Existence and uniqueness of a minimal solution are established in the case of a drift coefficient which is Lipschitz continuous in the state and gains processes and convex in the gains process. It is also shown that the minimal solution can be characterized as the unique solution of a functional stochastic control-type equation. This representation is related to the pena...
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作者：Shieh, NR
作者单位：National Taiwan University
摘要：Let X be a symmetric Levy process in R-d, d = 2, 3. We assume that X has independent alpha(j)-stable components, 1 < alpha(d) less than or equal to ... less than or equal to alpha(1) < 2 (a process with stable components, by Pruitt and Taylor), or more generally that X is d-dimensionally self-similar with similarity exponents H-j, H-j = 1/alpha(j) (a dilation-stable process, by Kunita). Let a given integer k greater than or equal to 2 be such that k(H - 1) < H, H = Sigma(j=1)(d) H-j. We prove ...
