In: Methodology and Computing in Applied Probability, 2013, vol. 15, no. 3, p. 485-509
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In: Methodology and Computing in Applied Probability, 2011, vol. 15, no. 3, p. 485-509
The interplay of fractal geometry, analysis and stochastics on the oneparameter sequence of self-similar generalized Sierpinski gaskets is studied. An improved algorithm for the exact computation of mean crossing times through the generating graphs SG(m) of generalized Sierpinski gaskets sg(m) for m up to 37 is presented and numerical approximations up to m = 100 are shown. Moreover, an...
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In: Stochastic Processes and their Applications, 2011, p. -
Stationary and isotropic iteration stable random tessellations are considered, which are constructed by a random process of iterative cell division. The collection of maximal polytopes at a fixed time t within a convex window View the MathML source is regarded and formulas for mean values, variances and a characterization of certain covariance measures are proved. The focus is on the case d≥3,...
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In: European congress of stereology and image analysis, ECS10, 2009, no. 10, p. 342-348
A new model for random tessellations having a fractal component is introduced. An explicit formula for the Hausdorff dimension is given and the exact gauge function of its Hausdorff measure is calculated. Moreover, fractal curvatures and mean fractal curvatures are considered. A theoretical result about the relation of these quantities is shown and is demonstrated numerically by an example.
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In: Image Analysis and Stereology, 2009, vol. 29, p. 69-76
Homogeneous planar tessellations stable under iteration (STIT tessellations) are considered. Using recent results about the joint distribution of direction and length of the typical I-, K- and J-segment we prove closed formulas for the first, second and higher moments of the length of these segments given their direction. This especially leads to the mean values and variances of these ...
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In: Applied Mathematical Sciences, 2009, vol. 38, p. 1885-1901
We study linear combinations of independent fractional Brownian motions and generalize several recent results from [10] and [17]. As a first new result we calculate explicitly the Hausdorff dimension of the sample paths of such processes. Moreover we compare different notions of fractional differentiability and calculate as a second new result explicitly the Cesáro fractional derivative of the...
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