Recently Lou and Wu obtained the formulas of pointwise dimensions of some Moran measures on Moran sets in Rd under the strong separation condition.In this paper,we prove that the result is still true under the open se...Recently Lou and Wu obtained the formulas of pointwise dimensions of some Moran measures on Moran sets in Rd under the strong separation condition.In this paper,we prove that the result is still true under the open set condition.Due to the lack of the strong separation condition,our approach is essentially different from that used by Lou and Wu.We also obtain the formulas of the Hausdorff and packing dimensions of the Moran measures and discuss some interesting examples.展开更多
Let BH,K = {BH,K(t), t ∈ R+} be a bifractional Brownian motion in Rd. This process is a selfsimilar Gaussian process depending on two parameters H and K and it constitutes a natural generalization of fractional Brown...Let BH,K = {BH,K(t), t ∈ R+} be a bifractional Brownian motion in Rd. This process is a selfsimilar Gaussian process depending on two parameters H and K and it constitutes a natural generalization of fractional Brownian motion (which is obtained for K = 1). The exact Hausdorff measures of the image, graph and the level set of BH,K are investigated. The results extend the corresponding results proved by Talagrand and Xiao for fractional Brownian motion.展开更多
In this paper,we get the formulas of upper(lower) pointwise dimensions of some Moran measures on Moran sets in Rd under the strong separation condition.We also obtain formulas for the dimension of the Moran measures.O...In this paper,we get the formulas of upper(lower) pointwise dimensions of some Moran measures on Moran sets in Rd under the strong separation condition.We also obtain formulas for the dimension of the Moran measures.Our results extend the known results of some self-similar measures and Moran measures studied by Cawley and Mauldin.展开更多
基金supported by National Natural Science Foundation of China (Grant No.11071082)the Fundamental Research Funds for the Central Universities,SCUT
文摘Recently Lou and Wu obtained the formulas of pointwise dimensions of some Moran measures on Moran sets in Rd under the strong separation condition.In this paper,we prove that the result is still true under the open set condition.Due to the lack of the strong separation condition,our approach is essentially different from that used by Lou and Wu.We also obtain the formulas of the Hausdorff and packing dimensions of the Moran measures and discuss some interesting examples.
基金supported by National Natural Science Foundation of China (Grant No.10721091)
文摘Let BH,K = {BH,K(t), t ∈ R+} be a bifractional Brownian motion in Rd. This process is a selfsimilar Gaussian process depending on two parameters H and K and it constitutes a natural generalization of fractional Brownian motion (which is obtained for K = 1). The exact Hausdorff measures of the image, graph and the level set of BH,K are investigated. The results extend the corresponding results proved by Talagrand and Xiao for fractional Brownian motion.
基金supported by National Natural Science Foundation of China (Grant No.10631040)
文摘In this paper,we get the formulas of upper(lower) pointwise dimensions of some Moran measures on Moran sets in Rd under the strong separation condition.We also obtain formulas for the dimension of the Moran measures.Our results extend the known results of some self-similar measures and Moran measures studied by Cawley and Mauldin.
