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作者：Bramson, Maury; Zeitouni, Ofer; Zerner, Martin P. W.
作者单位：University of Minnesota System; University of Minnesota Twin Cities; Technion Israel Institute of Technology; Technion Israel Institute of Technology; Eberhard Karls University of Tubingen; Stanford University; University of California System; University of California Davis
摘要：We construct forests that span Z(d), d >= 2, that are stationary and directed, and whose trees are infinite, but for which the subtrees attached to each vertex are as short as possible. For d >= 3, two independent copies of such forests, pointing in opposite directions, can be pruned so as to become disjoint. From this, we construct in d >= 3 a stationary, polynomially mixing and uniformly elliptic environment of nearest-neighbor transition probabilities on Z(d) for which the corresponding ran...
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作者：Dawson, D. A.; Li, Zenghu
作者单位：Carleton University; Beijing Normal University
摘要：A general affine Markov semigroup is formulated as the convolution of a homogeneous one with a skew convolution semigroup. We provide some sufficient conditions for the regularities of the homogeneous affine semigroup and the skew convolution semigroup. The corresponding affine Markov process is constructed as the strong solution of a system of stochastic equations with non-Lipschitz coefficients and Poisson-type integrals over some random sets. Based on this characterization, it is proved tha...
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作者：Peccati, Giovanni; Thieullen, Michele; Tudor, Ciprian A.
作者单位：Sorbonne Universite; Sorbonne Universite; Universite Paris Cite
摘要：Let the process {Y-t, t is an element of [0, 1]} have the form Y-t = delta(u1([o,t])), where delta stands for a Skorohod integral with respect to Brownian motion and u is a measurable process that verifies some suitable regularity conditions. We use a recent result by Tudor to prove that Y-t can be represented as the limit of linear combinations of processes that are products of forward and backward Brownian martingales. Such a result is a further step toward the connection between the theory ...
