Search results for " 60D05"

showing 3 items of 3 documents

Dimensions of random affine code tree fractals

2014

We calculate the almost sure Hausdorff dimension for a general class of random affine planar code tree fractals. The set of probability measures describing the randomness includes natural measures in random $V$-variable and homogeneous Markov constructions.

Discrete mathematicsCode (set theory)v-variable fractalsApplied MathematicsGeneral MathematicsProbability (math.PR)ta111Dynamical Systems (math.DS)self-similar setsTree (descriptive set theory)Box countingFractalIterated function systemMathematics - Classical Analysis and ODEsHausdorff dimensionClassical Analysis and ODEs (math.CA)FOS: MathematicsAffine transformationMathematics - Dynamical Systems28A80 60D05 37H99RandomnessMathematics - ProbabilityMathematics
researchProduct

Random cutout sets with spatially inhomogeneous intensities

2015

We study the Hausdorff dimension of Poissonian cutout sets defined via inhomogeneous intensity measures on Ahlfors-regular metric spaces. We obtain formulas for the Hausdorff dimension of such cutouts in self-similar and self-conformal spaces using the multifractal decomposition of the average densities for the natural measures.

General MathematicsStructure (category theory)Hausdorff dimensionDynamical Systems (math.DS)01 natural sciencesMeasure (mathematics)010104 statistics & probabilityCorollaryDimension (vector space)Classical Analysis and ODEs (math.CA)FOS: MathematicsMathematics::Metric Geometry0101 mathematicsMathematics - Dynamical SystemsMathematicsmatematiikkaHausdorffin dimensioProbability (math.PR)010102 general mathematicsMathematical analysisMultifractal systemPoissonian CutoutMetric spaceMathematics - Classical Analysis and ODEsHausdorff dimensionPrimary 60D05 Secondary 28A80 37D35 37C45Intensity (heat transfer)Mathematics - Probability
researchProduct

The second-order analysis of marked spatio-temporal point processes, with an application to earthquake data

2016

To analyse interaction in marked spatio-temporal point processes (MSTPPs), we introduce marked (cross) second-order reduced moment measures and K-functions for general inhomogeneous second-order intensity reweighted stationary MSTPPs. These summary statistics, which allow us to quantify dependence between different mark categories of the points, are depending on the specific mark space and mark reference measure chosen. We also look closer at how the summary statistics reduce under assumptions such as the MSTPP being multivariate and/or stationary. A new test for independent marking is devised and unbiased minus-sampling estimators are derived for all statistics considered. In addition, we …

Methodology (stat.ME)FOS: Computer and information sciences60G55 60D05 62M30Statistics - Methodology
researchProduct