共查询到20条相似文献,搜索用时 31 毫秒
1.
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
2.
Jiang-Lun Wu 《Journal of Mathematical Analysis and Applications》2007,330(1):133-143
In this paper, a nonstandard construction of generalized white noise is established. This provides a (hyperfinite) flat integral representation of probability measures for generalized random fields derived as image probability measures of generalized white noise under certain measurable transformations, including Euclidean random fields obtained as convolution from generalized white noise with Euclidean kernels. 相似文献
3.
Enkelejd Hashorva Oleg Seleznjev Zhongquan Tan 《Journal of Mathematical Analysis and Applications》2018,457(1):841-867
This contribution is concerned with Gumbel limiting results for supremum with centered Gaussian random fields with continuous trajectories. We show first the convergence of a related point process to a Poisson point process thereby extending previous results obtained in [8] for Gaussian processes. Furthermore, we derive Gumbel limit results for as and show a second-order approximation for for any . 相似文献
4.
Youri Davydov Ričardas Zitikis 《Annals of the Institute of Statistical Mathematics》2008,60(2):345-365
We suggest simple and easily verifiable, yet general, conditions under which multi-parameter stochastic processes converge
weakly to a continuous stochastic process. Connections to, and extensions of, R. Dudley’s results play an important role in
our considerations, and we therefore discuss them in detail. As an illustration of general results, we consider multi-parameter
stochastic processes that can be decomposed into differences of two coordinate-wise non-decreasing processes, in which case
the aforementioned conditions become even simpler. To illustrate how the herein developed general approach can be used in
specific situations, we present a detailed analysis of a two-parameter sequential empirical process. 相似文献
5.
Let X = {X(t), t ∈ ℝ
N
} be a Gaussian random field with values in ℝ
d
defined by
. The properties of space and time anisotropy of X and their connections to uniform Hausdorff dimension results are discussed. It is shown that in general the uniform Hausdorff
dimension result does not hold for the image sets of a space-anisotropic Gaussian random field X.
When X is an (N, d)-Gaussian random field as in (1), where X
1,...,X
d
are independent copies of a real valued, centered Gaussian random field X
0 which is anisotropic in the time variable. We establish uniform Hausdorff dimension results for the image sets of X. These results extend the corresponding results on one-dimensional Brownian motion, fractional Brownian motion and the Brownian
sheet.
相似文献
((1)) |
6.
Jon Aaronson 《Proceedings Mathematical Sciences》1994,104(2):413-419
We show that the Cauchy random walk on the line, and the Gaussian random walk on the plane are similar as infinite measure
preserving transformations. 相似文献
7.
8.
Approximation complexity of additive random fields 总被引:1,自引:0,他引:1
9.
Ali Reza Taheriyoun 《Statistics & probability letters》2012,82(3):606-613
In many problems, a specific function like h(⋅) is considered as the covariance function. Based on the asymptotic distribution of the periodogram and Euler characteristic, three methods are introduced to test the equality of the covariance function with h(⋅). Our analyses prove the accuracy of the power and scaling laws for the covariance function of metal surfaces. 相似文献
10.
《Applied and Computational Harmonic Analysis》2020,48(1):293-320
Operator scaling Gaussian random fields, as anisotropic generalizations of self-similar fields, know an increasing interest for theoretical studies in the literature. However, up to now, they were only defined through stochastic integrals, without explicit covariance functions. In this paper we exhibit explicit covariance functions, as anisotropic generalizations of fractional Brownian fields ones, and define corresponding Operator scaling Gaussian random fields. This allows us to propose a fast and exact method of simulation in dimension 2 based on the circulant embedding matrix method, following ideas of Stein [34] for fractional Brownian surfaces syntheses. This is a first piece of work to popularize these models in anisotropic spatial data modeling. 相似文献
11.
We refine some well-known approximation theorems in the theory of homogeneous lattice random fields. In particular, we prove that every translation invariant Borel probability measure on the space X of finite-alphabet configurations on d, d1, can be weakly approximated by Markov measures n with supp(n)=X and with the entropies h(n)h(). The proof is based on some facts of Thermodynamic Formalism; we also present an elementary constructive proof of a weaker version of this theorem.Mathematics Subject Classifications (2000): Primary 28D20, 37C85, 60G60; secondary 82B20Dedicated to Professor A. I. Vorobyov, member of the Russian Academy of Sciences and Director of the Hematology Research Center of the Russian Academy of Medical Sciences, on the occasion of his 75th birthday 相似文献
12.
This paper studies a class of Gaussian random fields defined on lattices that arise in pattern analysis. Phase transitions are shown to exist at a critical temperature for these Gaussian random fields. These are established by showing discontinuous behavior for certain field random variables as the lattice size increases to infinity. The discontinuities in the statistical behavior of these random variables occur because the growth rates of the eigenvalues of the inverse of the variance-covariance matrix at the critical temperature are different from the growth rates at noncritical temperatures. It is also shown that the limiting specific heat has a phase transition with a power law behavior. The critical temperature occurs at the end point of the available values of temperature. Thus, although the critical behavior is not extreme, caution should be exercised when using such models near critical temperatures.Research supported by AFOSR Grant No. 91-0048 and by USARO Grant No. DAAL03-90-G-0103. 相似文献
13.
14.
15.
We study properties of random fields that form conditional bases and their applications in spatial statistics. 相似文献
16.
Saroj Kumar Dash 《Journal of Mathematical Analysis and Applications》2008,339(1):98-107
For a symmetric stable process X(t,ω) with index α∈(1,2], f∈Lp[0,2π], p?α, and , we establish that the random Fourier-Stieltjes (RFS) series converges in the mean to the stochastic integral , where fβ is the fractional integral of order β of the function f for . Further it is proved that the RFS series is Abel summable to . Also we define fractional derivative of the sum of order β for an, An(ω) as above and . We have shown that the formal fractional derivative of the series of order β exists in the sense of mean. 相似文献
17.
Let M be a random (n×n)-matrix over GF[q] such that for each entry Mij in M and for each nonzero field element α the probability Pr[Mij=α] is p/(q−1), where p=(log n−c)/n and c is an arbitrary but fixed positive constant. The probability for a matrix entry to be zero is 1−p. It is shown that the expected rank of M is n−𝒪(1). Furthermore, there is a constant A such that the probability that the rank is less than n−k is less than A/qk. It is also shown that if c grows depending on n and is unbounded as n goes to infinity, then the expected difference between the rank of M and n is unbounded. © 1997 John Wiley & Sons, Inc. Random Struct. Alg., 10 , 407–419, 1997 相似文献
18.
If X is a point random field on d then convergence in distribution of the renormalization Cλ|Xλ ? αλ| as λ → ∞ to generalized random fields is examined, where Cλ > 0, αλ are real numbers for λ > 0, and Xλ(f) = λ?dX(fλ) for . If such a scaling limit exists then Cλ = λθg(λ), where g is a slowly varying function, and the scaling limit is self-similar with exponent θ. The classical case occurs when and the limit process is a Gaussian white noise. Scaling limits of subordinated Poisson (doubly stochastic) point random fields are calculated in terms of the scaling limit of the environment (driving random field). If the exponent of the scaling limit is then the limit is an independent sum of the scaling limit of the environment and a Gaussian white noise. If the scaling limit coincides with that of the environment while if the limit is Gaussian white noise. Analogous results are derived for cluster processes as well. 相似文献
19.
We provide a characterization of compactness in the spaceD of functions of two variables defined on a unit square. The functions fromD have the property that their discontinuity points lie on smooth curves. Conditions for the tightness of probability measures inD and conditions for weak convergence of random fields with trajectories inD are derived. Vilnius Gediminas Technical University, Saulétekio 11; Institute of Mathematics and Informatics, Akademijos 4, 2600 Vilnius, Lithuania. Translated from Lietuvos Matematikos Rinkinys, Vol. 39, No. 2, pp 169–184, April–June, 1999. Translated by R. Banys 相似文献