There are mainly two approaches to the multifractal analysis of measures. The first one,which is used in applications and in studying problems arising from dynamical systems,uses a hierarchy of boxes. The second one,w...There are mainly two approaches to the multifractal analysis of measures. The first one,which is used in applications and in studying problems arising from dynamical systems,uses a hierarchy of boxes. The second one,which is more satisfactory from the viewpoint of geometric measure theory,uses more intrinsic concepts. This article is an account of a work by J.Barral,F.Ben Nasr,and J.Peyriére [3] which provides a bridge between these two theories.展开更多
The mulfifractal formalism for single measure is reviewed. Next, a mixed generalized multifractal formalism is introduced which extends the multifractal formalism of a single measure based on generalizations of the Ha...The mulfifractal formalism for single measure is reviewed. Next, a mixed generalized multifractal formalism is introduced which extends the multifractal formalism of a single measure based on generalizations of the Hausdorff and packing measures to a vector of simultaneously many measures. Borel-Cantelli and Large deviations Theorems are extended to higher orders and thus applied for the validity of the new variant of the multifractal formalism for some special cases of multi-doubling type measures.展开更多
In this paper,we compare the mutual multifractal Renyi dimensions to the´mutual multifractal Hausdorff and pre-packing dimensions.We also provide a relationship between the mutual multifractal Renyi dimensions of...In this paper,we compare the mutual multifractal Renyi dimensions to the´mutual multifractal Hausdorff and pre-packing dimensions.We also provide a relationship between the mutual multifractal Renyi dimensions of orthogonal projections´of a couple of measures(µ,ν)in R^(n).As an application,we study the mutual multifractal analysis of the projections of measures.展开更多
The multifractal formalism is shown to hold for a class of Moran measures supported on the Moran fractals associated with the sequences of which the frequency of the letter exists.
The main goal of this paper is to study the sample path properties for the harmonisable-type N-parameter multifractional Brownian motion, whose local regularities change as time evolves. We provide the upper and lower...The main goal of this paper is to study the sample path properties for the harmonisable-type N-parameter multifractional Brownian motion, whose local regularities change as time evolves. We provide the upper and lower bounds on the hitting probabilities of an （N, d）-multifractional Brownian motion. Moreover, we determine the Hausdorff dimension of its inverse images, and the Hausdorff and packing dimensions of its level sets.展开更多
文摘There are mainly two approaches to the multifractal analysis of measures. The first one,which is used in applications and in studying problems arising from dynamical systems,uses a hierarchy of boxes. The second one,which is more satisfactory from the viewpoint of geometric measure theory,uses more intrinsic concepts. This article is an account of a work by J.Barral,F.Ben Nasr,and J.Peyriére [3] which provides a bridge between these two theories.
文摘The mulfifractal formalism for single measure is reviewed. Next, a mixed generalized multifractal formalism is introduced which extends the multifractal formalism of a single measure based on generalizations of the Hausdorff and packing measures to a vector of simultaneously many measures. Borel-Cantelli and Large deviations Theorems are extended to higher orders and thus applied for the validity of the new variant of the multifractal formalism for some special cases of multi-doubling type measures.
文摘In this paper,we compare the mutual multifractal Renyi dimensions to the´mutual multifractal Hausdorff and pre-packing dimensions.We also provide a relationship between the mutual multifractal Renyi dimensions of orthogonal projections´of a couple of measures(µ,ν)in R^(n).As an application,we study the mutual multifractal analysis of the projections of measures.
基金supported by the National Natural Science Foundation of China(Grant No.10171028)the Special for Major State Basic Research Projects of China.
文摘The multifractal formalism is shown to hold for a class of Moran measures supported on the Moran fractals associated with the sequences of which the frequency of the letter exists.
基金Supported by Zhejiang Provincial Natural Science Foundation of China (Grant No. Y6100663)
文摘The main goal of this paper is to study the sample path properties for the harmonisable-type N-parameter multifractional Brownian motion, whose local regularities change as time evolves. We provide the upper and lower bounds on the hitting probabilities of an （N, d）-multifractional Brownian motion. Moreover, we determine the Hausdorff dimension of its inverse images, and the Hausdorff and packing dimensions of its level sets.
