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作者：Bressaud, X.; Maass, A.; Martinez, S.; San Martin, J.
作者单位：Aix-Marseille Universite; Universidad de Chile
摘要：We study the standard property of the natural filtration associated to a 0-1 valued stationary process. In our main result we show that if the process has summable memory decay, then the associated filtration is standard. We prove it by coupling techniques. For a process whose associated filtration is standard, we construct a product type filtration extending it, based upon the usual couplings and the Vershik's criterion for standardness.
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作者：Brossard, Jean; Leuridan, Christophe
作者单位：Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
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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 ...
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作者：Feng, J
作者单位：University of Massachusetts System; University of Massachusetts Amherst
摘要：Large deviation for Markov processes can be studied by Hamilton-Jacobi equation techniques. The method of proof involves three steps: First, we apply a nonlinear transform to generators of the Markov processes, and verify that limit of the transformed generators exists. Such limit induces a Hamilton-Jacobi equation. Second, we show that a strong form of uniqueness (the comparison principle) holds for the limit equation. Finally, we verify an exponential compact containment estimate. The large ...
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作者：Comets, Francis; Yoshida, Nobuo
作者单位：Universite Paris Cite; Kyoto University
摘要：In this paper we consider directed polymers in random environment with discrete space and time. For transverse dimension at least equal to 3, we prove that diffusivity holds for the path in the full weak disorder region, that is, where the partition function differs from its annealed value only by a non-vanishing factor. Deep inside this region, we also show that the quenched averaged energy has fluctuations of order 1. In complete generality (arbitrary dimension and temperature), we prove mon...
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作者：Adams, Stefan; Bru, Jean-Bernard; Koenig, Wolfgang
作者单位：Max Planck Society; Dublin Institute for Advanced Studies; Johannes Gutenberg University of Mainz; Leipzig University
摘要：We introduce two probabilistic models for N interacting Brownian motions moving in a trap in R-d under mutually repellent forces. The two models are defined in terms of transformed path measures on finite time intervals under a trap Hamiltonian and two respective pair-interaction Hamiltonians. The first pair interaction exhibits a particle repellency, while the second one imposes a path repellency. We analyze both models in the limit of diverging time with fixed number N of Brownian motions. I...
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作者：Tanner, Steve
作者单位：Eastern Oregon University
摘要：Let u be a pluriharmonic function on the unit ball in C-n. I consider the relationship between the set of points L-u on the boundary of the ball at which u converges nontangentially and the set of points L-u at which u converges along conditioned Brownian paths. For harmonic functions u of two variables, the result L-u (a.e.)= L-u has been known for some time, as has a counterexample to the same equality for three variable harmonic functions. I extend the L-u (a.e.)= result to pluriharmonic fu...
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作者：Broman, EI
作者单位：Chalmers University of Technology
摘要：Given a trigonometric polynomial f : [0, 1] -> [0, 1] of degree m, one can define a corresponding stationary process {X-i}(i is an element of Z) via determinants of the Toeplitz matrix for f. We show that for m = 1 this process, which is trivially one-dependent, is a two-block-factor.
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作者：Adler, M; van Moerbeke, P
作者单位：Brandeis University
摘要：In a celebrated paper, Dyson shows that the spectrum of an n x n random Hermitian matrix, diffusing according to an Ornstein-Uhlenbeck process, evolves as n noncolliding Brownian motions held together by a drift term. The universal edge and bulk scalings for Hermitian random matrices, applied to the Dyson process, lead to the Airy and Sine processes. In particular, the Airy process is a continuous stationary process, describing the motion of the outermost particle of the Dyson Brownian motion,...
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作者：Taylor, J; Takemura, A; Adler, RJ
作者单位：Stanford University; University of Tokyo; Technion Israel Institute of Technology
摘要：We study the accuracy of the expected Euler characteristic approximation to the distribution of the maximum of a smooth, centered, unit variance Gaussian process f. Using a point process representation of the error, valid for arbitrary smooth processes, we show that the error is in general exponentially smaller than any of the terms in the approximation. We also give a lower bound on this exponential rate of decay in terms of the maximal variance of a family of Gaussian processes f(x), derived...
