Attainable densities for random maps

Densities for Random Balanced Sampling

A random balanced sample (RBS) is a multivariate distribution with n components Xk, each uniformly distributed on [−1, 1], such that the sum of these components is precisely 0. The corresponding vectors ~ X lie in an (n − 1)–dimensional polytope M(n). We present new methods for the construction of such RBS via densities over M(n) and these apply for arbitrary n. While simple densities had been ...

Mechanisms for Phase Transitions in the Multifractal Analysis of Invariant Densities of Correlated Random Maps *

für Naturforschung in cooperation with the Max Planck Society for the Advancement of Science under a Creative Commons Attribution 4.0 International License. Dieses Werk wurde im Jahr 2013 vom Verlag Zeitschrift für Naturforschung in Zusammenarbeit mit der Max-Planck-Gesellschaft zur Förderung der Wissenschaften e.V. digitalisiert und unter folgender Lizenz veröffentlicht: Creative Commons Namen...

Wavelet-Based Random Densities

In this paper we describe the theoretical properties of wavelet based random densities and present algorithms for their generation. We exhibit random densities subject to some standard constraints: smoothness , symmetry, unimodality, and skewness. We also provide three relevant applications of wavelet based-random densities.

Synthesizing Chaotic Maps with Prescribed Invariant Densities

The Inverse Frobenius-Perron problem (IFPP) concerns the creation of discrete chaotic mappings with arbitrary invariant densities. In this note, we present a new and elegant solution to the IFPP, based on positive matrix theory. Our method allows chaotic maps with arbitrary piecewise-constant invariant densities, and with arbitrary mixing properties, to be synthesized.

Orthonormal Expansions of Invariant Densities for Expanding Maps