共查询到20条相似文献,搜索用时 15 毫秒
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设犡是一完备可分度量空间,犓(ω)为Graf随机模型下的随机递归集.该文构造了一列随机不变测度μ狀(狀≥1),它们是Hutchinson确定模型下不变测度的推广;证明了存在一随机概率测度μ ,使得Suppμ =犓(ω)且μ狀→μ (狀→∞)(弱收敛);得到了μ狀的一些局部性质. 相似文献
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Toshiro Watanabe 《Journal of Theoretical Probability》2002,15(3):631-665
Natural examples of increasing shift self-similar additive random sequences are constructed, which are associated with supercritical branching processes. The rate of growth and the distributional properties of them are studied in terms of the offspring distributions of the supercritical branching processes. The results are applied to two types of laws of the iterated logarithm for a Brownian motion on the unbounded Sierpinski gasket. An extension of the Bingham–Doney–de Meyer theorem on the limits of supercritical branching processes is also proved. 相似文献
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Russian Mathematics - The article describes a new type of Gaussian fields on a two-dimensional 2-adic space, invariant under the translation group and group of scaling transformations (self-similar... 相似文献
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Julien Barral 《Journal of Theoretical Probability》2000,13(4):1027-1060
Until now [see Kahane;(19) Holley and Waymire;(16) Falconer;(14) Olsen;(29) Molchan;(28) Arbeiter and Patzschke;(1) and Barral(3)] one determines the multifractal spectrum of a statistically self-similar positive measure of the type introduced, in particular by Mandelbrot,(26, 27) only in the following way: let be such a measure, for example on the boundary of a c-ary tree equipped with the standard ultrametric distance; for 0, denote by E
the set of the points where possesses a local Hölder exponent equal to , and dim E
the Hausdorff dimension of E
; then, there exists a deterministic open interval I
*+ and a function f: I
*+ such that for all in I, with probability one, dim E
=f(). This statement is not completely satisfactory. Indeed, the main result in this paper is: with probability one, for all I, dim E
=f(). This holds also for a new type of statistically self-similar measures deduced from a result recently obtained by Liu.(22) We also study another problem left open in the previous works on the subject: if =inf(I) or =sup(I), one does not know whether E
is empty or not. Under suitable assumptions, we show that E
ø and calculate dim E
. 相似文献
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多型随机递归集关于统计自相似测度的Multifractal分解 总被引:2,自引:0,他引:2
本文构造了一类多型随机递归集K,并利用Falconer的方法[1]获得了K的重分形分解集Kα(α>0)的Hausdorff维数和Packing维数. 相似文献
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Self-Similar Lattice Tilings 总被引:12,自引:0,他引:12
We study the general question of the existence of self-similar lattice tilings of Euclidean space. A necessary and sufficient
geometric condition on the growth of the boundary of approximate tiles is reduced to a problem in Fourier analysis that is
shown to have an elegant simple solution in dimension one. In dimension two we further prove the existence of connected self-similar
lattice tilings for parabolic and elliptic dilations. These results apply to produce Haar wavelet bases and certain canonical
number systems. 相似文献
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We investigate computability of a self-similar set on a Euclidean space. A nonempty compact subset of a Euclidean space is called a self-similar set if it equals to the union of the images of itself by some set of contractions. The main result in this paper is that if all of the contractions are computable, then the self-similar set is a recursive compact set. A further result on the case that the self-similar set forms a curve is also discussed. 相似文献
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Normal and Non-Normal Points of Self-Similar Sets and Divergence Points of Self-Similar Measures 总被引:6,自引:0,他引:6
Let K and µ be the self-similar set and the self-similarmeasure associated with an IFS (iterated function system) withprobabilities (Si, pi)i=1,...,N satisfying the open set condition.Let ={1,...,N}N denote the full shift space and let : K denotethe natural projection. The (symbolic) local dimension of µat is defined by limn (log µK|n/log diam K|n), where for = (1, 2,...) . A point for which the limit limn (log µK|n/log diam K|n) doesnot exist is called a divergence point. In almost all of theliterature the limit limn (log µK|n/log diam K|n) is assumedto exist, and almost nothing is known about the set of divergencepoints. In the paper a detailed analysis is performed of theset of divergence points and it is shown that it has a surprisinglyrich structure. For a sequence (n)n, let A(n) denote the setof accumulation points of (n)n. For an arbitrary subset I ofR, the Hausdorff and packing dimension of the set
and related sets is computed. An interesting and surprisingcorollary to this result is that the set of divergence pointsis extremely visible; it can be partitioned intoan uncountable family of pairwise disjoint sets each with fulldimension. In order to prove the above statements the theory of normaland non-normal points of a self-similar set is formulated anddeveloped in detail. This theory extends the notion of normaland non-normal numbers to the setting of self-similar sets andhas numerous applications to the study of the local propertiesof self-similar measures including a detailed study of the setof divergence points. 相似文献
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Boscolo S. Turitsyn S. K. Novokshenov V. Yu. Nijhof J. H. B. 《Theoretical and Mathematical Physics》2002,133(3):1647-1656
We study solutions of the nonlinear Schrödinger equation (NLSE) with gain, describing optical pulse propagation in an amplifying medium. We construct a semiclassical self-similar solution with a parabolic temporal variation that corresponds to the energy-containing core of the asymptotically propagating pulse in the amplifying medium. We match the self-similar core through Painlevé functions to the solution of the linearized equation that corresponds to the low-amplitude tails of the pulse. The analytic solution accurately reproduces the numerically calculated solution of the NLSE. 相似文献
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本文讨论一类(包括Koch曲线在内的)自相似曲线,证明了其上的简单曲线是Whitney型临界集,并在微小扰动下仍是简单曲线. 相似文献
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关于自相似集的Hausdorff测度 总被引:12,自引:0,他引:12
得到了 Hausdorff容度与 Hausdorff测度相等的集的充分必要条件.对于满足开集条件的自相似集,验证了它的Hausdorff容度与Hausdorf测度相等并给出了它的Hausdorff测度的一个便于应用的公式.作为例子,给出了均匀康托集的Hausdorff测度的一种新的计算方法,对于Koch曲线的Hausdorff测度的上限也作了讨论. 相似文献
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Multifractal Decomposition of Statistically Self-Similar Sets 总被引:1,自引:0,他引:1
Let K be a statistically self-similar set defined by Graf. In this paper, we construct a random measure ρ which is supported by
K and study the multifractal decomposition for K with ρ. Under such a decomposition, we obtain the expression of the spectrum function ƒ(α).
Received July 18, 1997, Accepted October 13, 2000 相似文献
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统计自相似集的重分形分解 总被引:3,自引:0,他引:3
设K是由Graf定义的统计自相似集.本文构造了一支撑在K上的随机测 度p,并研究了结合P的K的重分形分解,得到了分形谱函数f(α)的表达式. 相似文献
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Group self-similar processes are introduced. The spectral representation of such processes in the class of multidimensional strictly stable processes is determined. The uniqueness of such representations in terms of the corresponding group actions and cocycles is established. 相似文献