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作者：Zhang, Yu
作者单位：University of Colorado System; University of Colorado at Colorado Springs
摘要：We consider the first passage percolation model on Z(2). In this model, we assign independently to each edge e a passage time t(e) with a common distribution F. Let T(u, v) be the passage time from u to v. In this paper, we show that, whenever F(0) < p(c), sigma(2)(T((0, 0), (n, 0))) >= C log n for all n >= 1. Note that if F satisfies an additional special condition, inf supp(F) = r > 0 and F(r) > (p) over right arrow (c), it is known that there exists M such that for all n, sigma(2)(T((0, 0),...
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作者：Pete, Gabor
作者单位：Microsoft
摘要：We consider a four-vertex model introduced by Balint Toth: a dependent bond percolation model on Z(2) in which every edge is present with probability 1/2 and each vertex has exactly two incident edges, perpendicular to each other. We prove that all components are finite cycles almost surely, but the expected diameter of the cycle containing the origin is infinite. Moreover, we derive the following critical exponents; the tail probability P(diameter of the cycle of the origin > n) approximate t...
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作者：Wu, Xian-Yuan; Zuang, Yu
作者单位：Capital Normal University; University of Colorado System; University of Colorado at Colorado Springs
摘要：We consider the supercritical oriented percolation model. Let K be all the percolation points. For each u is an element of K, we write Y-u as its rightmost path. Let G = U-u y(u). In this paper, we show that G is a single tree with only one topological end. We also present a relationship between X and G and construct a bijection between K and Z using the preorder traversal algorithm. Through applications of this fundamental graph property, we show the uniqueness of an infinite oriented cluster...
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作者：Bryc, Wlodzimierz; Matysiak, Wojciech; Wesolowski, Jacek
作者单位：University System of Ohio; University of Cincinnati; Warsaw University of Technology
摘要：This paper is a continuation of our previous research on quadratic harnesses, that is, processes with linear regressions and quadratic conditional variances. Our main result is a construction of a Markov process from given orthogonal and martingale polynomials. The construction uses a two-parameter extension of the Al-Salam-Chihara polynomials and a relation between these polynomials for different values of parameters.
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作者：Kontorovich, Leonid (Aryeh); Ramanan, Kavita
作者单位：Weizmann Institute of Science; Carnegie Mellon University
摘要：The martingale method is used to establish concentration inequalities for a class of dependent random sequences on a countable state space, with the constants in the inequalities expressed in terms of certain mixing coefficients. Along the way, bounds are obtained oil martingale differences associated with the random sequences, which may be of independent interest. As applications of the main result, concentration inequalities are also derived for inhomogeneous Markov chains and hidden Markov ...
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作者：Dolgopyat, Dmitry; Keller, Gerhard; Liverani, Carlangelo
作者单位：University System of Maryland; University of Maryland College Park; University of Erlangen Nuremberg; University of Rome Tor Vergata
摘要：We prove a quenched central limit theorem for random walks with bounded increments in a randomly evolving, environment on Z(d). We assume that the transition probabilities of the walk depend not too strongly on the environment and that the evolution of the environment is Markovian with strong spatial and temporal mixing properties.
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作者：Karatzas, Ioannis; Zamfirescu, Ingrid-Mona
作者单位：Columbia University; City University of New York (CUNY) System; Baruch College (CUNY)
摘要：We develop a martingale approach for studying continuous-time stochastic differential games of control and stopping, in a non-Markovian framework and with the control affecting only the drift term of the state-process. Under appropriate conditions, we show that the game has a value and construct a saddle pair of optimal control and stopping strategies. Crucial in this construction is a characterization of saddle pairs in terms of pathwise and martingale properties of suitable quantities.
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作者：Chen, Z. -Q.; Fitzsimmons, P. J.; Kuwae, K.; Zhang, T. -S.
作者单位：University of Washington; University of Washington Seattle; University of California System; University of California San Diego; Kumamoto University; University of Manchester
摘要：Using time-reversal, we introduce a stochastic integral for zero-energy additive functionals of symmetric Markov processes, extending earlier work of S. Nakao. Various properties of such stochastic integrals are discussed and an Ito formula for Dirichlet processes is obtained.
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作者：Sole, Josep Lluis; Utzet, Frederic
作者单位：Autonomous University of Barcelona
摘要：Let X = {X-t, t >= 0} be a cadlag Levy process, centered, with moments of all orders. There are two families of orthogonal polynomials associated with X. On one hand, the Kailath-Segall formula gives the relationship between the iterated integrals and the variations of order n of X, and defines a family of polynomials P-1(x(t)), P-2(x(1), x(2)).... that are orthogonal with respect to the joint law of the variations of X. On the other hand, we can F construct a sequence of orthogonal polynomial...
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作者：Zhan, Dapeng
作者单位：University of California System; University of California Berkeley
摘要：We prove that the chordal SLE kappa trace is reversible for kappa is an element of (0, 4].
