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Ercan Sönmez 《Stochastic Processes and their Applications》2018,128(2):426-444
Let be a multivariate operator-self-similar random field with values in . Such fields were introduced in [22] and satisfy the scaling property for all , where is a real matrix and is an real matrix. We solve an open problem in [22] by calculating the Hausdorff dimension of the range and graph of a trajectory over the unit cube in the Gaussian case. In particular, we enlighten the property that the Hausdorff dimension is determined by the real parts of the eigenvalues of and as well as the multiplicity of the eigenvalues of and . 相似文献
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Payman Eskandari 《Comptes Rendus Mathematique》2018,356(3):312-315
Let X be a Riemann surface of positive genus. Denote by the configuration space of n distinct points on X. We use the Betti–de Rham comparison isomorphism on to define an integrable connection on the trivial vector bundle on with fiber the universal algebra of the Lie algebra associated with the descending central series of of . The construction is inspired by the Knizhnik–Zamolodchikov system in genus zero and its integrability follows from Riemann period relations. 相似文献
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We consider a -dimensional random field that solves a system of elliptic stochastic equations on a bounded domain , with additive white noise and spatial dimension . Properties of and its probability law are proved. For Gaussian solutions, using results from Dalang and Sanz-Solé (2009), we establish upper and lower bounds on hitting probabilities in terms of the Hausdorff measure and Bessel–Riesz capacity, respectively. This relies on precise estimates of the canonical distance of the process or, equivalently, on estimates of increments of the Green function of the Laplace equation. 相似文献
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Christophe Cuny Jérôme Dedecker Florence Merlevède 《Stochastic Processes and their Applications》2018,128(4):1347-1385
The famous results of Komlós, Major and Tusnády (see Komlós et al., 1976 [15] and Major, 1976 [17]) state that it is possible to approximate almost surely the partial sums of size of i.i.d. centered random variables in () by a Wiener process with an error term of order . Very recently, Berkes et al. (2014) extended this famous result to partial sums associated with functions of an i.i.d. sequence, provided a condition on a functional dependence measure in is satisfied. In this paper, we adapt the method of Berkes, Liu and Wu to partial sums of functions of random iterates. Taking advantage of the Markovian setting, we shall give new dependent conditions, expressed in terms of a natural coupling (in or in ), under which the strong approximation result holds with rate . As we shall see our conditions are well adapted to a large variety of models, including left random walks on , contracting iterated random functions, autoregressive Lipschitz processes, and some ergodic Markov chains. We also provide some examples showing that our -coupling condition is in some sense optimal. 相似文献
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We investigate the regularity of random attractors for the non-autonomous non-local fractional stochastic reaction–diffusion equations in with . We prove the existence and uniqueness of the tempered random attractor that is compact in and attracts all tempered random subsets of with respect to the norm of . The main difficulty is to show the pullback asymptotic compactness of solutions in due to the noncompactness of Sobolev embeddings on unbounded domains and the almost sure nondifferentiability of the sample paths of the Wiener process. We establish such compactness by the ideas of uniform tail-estimates and the spectral decomposition of solutions in bounded domains. 相似文献
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Jüri Lember Heinrich Matzinger Joonas Sova Fabio Zucca 《Stochastic Processes and their Applications》2018,128(5):1678-1710
Let and be random sequences taking values in a finite set . We consider a similarity score that measures the homology of words and . A typical example is the length of the longest common subsequence. We study the order of moment in the case where the two-dimensional process is a Markov chain on . This general model involves independent Markov chains, hidden Markov models, Markov switching models and many more. Our main result establishes a condition that guarantees that . We also perform simulations indicating the validity of the condition. 相似文献
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Let q be a positive integer. Recently, Niu and Liu proved that, if , then the product is not a powerful number. In this note, we prove (1) that, for any odd prime power ? and , the product is not a powerful number, and (2) that, for any positive odd integer ?, there exists an integer such that, for any positive integer , the product is not a powerful number. 相似文献
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A second order asymptotic expansion in the local limit theorem for a simple branching random walk in
Zhi-Qiang Gao 《Stochastic Processes and their Applications》2018,128(12):4000-4017
Consider a branching random walk, where the underlying branching mechanism is governed by a Galton–Watson process and the migration of particles by a simple random walk in . Denote by the number of particles of generation located at site . We give the second order asymptotic expansion for . The higher order expansion can be derived by using our method here. As a by-product, we give the second order expansion for a simple random walk on , which is used in the proof of the main theorem and is of independent interest. 相似文献
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In this paper, we establish the precise asymptotic behaviors of the tail probability and the transition density of a large class of isotropic Lévy processes when the scaling order is between 0 and 2 including 2. We also obtain the precise asymptotic behaviors of the tail probability of subordinators when the scaling order is between 0 and 1 including 1.The asymptotic expressions are given in terms of the radial part of characteristic exponent and its derivative. In particular, when varies regularly, as the tail probability is asymptotically equal to a constant times 相似文献
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Andrea Luigi Tironi 《Discrete Mathematics》2018,341(11):3152-3158
Let be a hypersurface in with defined over a finite field of elements. In this note, we classify, up to projective equivalence, hypersurfaces as above which reach two elementary upper bounds for the number of -points on which involve a Thas’ invariant. 相似文献
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In this paper, we consider the Cauchy problem for a two-phase model with magnetic field in three dimensions. The global existence and uniqueness of strong solution as well as the time decay estimates in are obtained by introducing a new linearized system with respect to for constants and , and doing some new a priori estimates in Sobolev Spaces to get the uniform upper bound of in norm. 相似文献