Topology-guided sampling of nonhomogeneous random processes

Topology-Guided Sampling of Nonhomogeneous Random Fields

Topological measurements are increasingly being accepted as an important tool for quantifying complex structures. In many applications these structures can be expressed as nodal domains of real-valued functions and are obtained only through experimental observation or numerical simulations. In both cases, the data on which the topological measurements are based are derived via some form of fini...

Random Sampling of Random Processes: Stationary Point Processes

This is the first of a series of papers treating randomly sampled random processes. Spectral analysis of the resulting samples presupposes knowledge of the statistics of 1 t~}, the random point process whose variates represent the sampling times. We introduce a class of s ta t ionary point processes, whose s ta t ionar i ty (as characterized by any of several equivalent criteria) leads to wide-...

Random sampling of long-memory stationary processes

This paper investigates the second order properties of a stationary process after random sampling. While a short memory process gives always rise to a short memory one, we prove that long-memory can disappear when the sampling law has heavy enough tails. We prove that under rather general conditions the existence of the spectral density is preserved by random sampling. We also investigate the e...

Generating Nonhomogeneous Poisson Processes

We present an overview of existing methods to generate pseudorandom numbers from a nonhomogeneous Poisson process. We start with various definitions of the nonhomogeneous Poisson process, present theoretical results (sometimes with a proof) that form the basis of existing generation algorithms, and provide algorithm listings. Whenever available, we also provide links to sources containing compu...

Random Distributions, Random Affine Systems, Sampling of Renewal Processes