Concept
Stochastic geometry
Related concepts (7)
Poisson point process
In probability, statistics and related fields, a Poisson point process is a type of random mathematical object that consists of points randomly located on a mathematical space with the essential feature that the points occur independently of one another. The Poisson point process is often called simply the Poisson process, but it is also called a Poisson random measure, Poisson random point field or Poisson point field.
Moment measure
In probability and statistics, a moment measure is a mathematical quantity, function or, more precisely, measure that is defined in relation to mathematical objects known as point processes, which are types of stochastic processes often used as mathematical models of physical phenomena representable as randomly positioned points in time, space or both. Moment measures generalize the idea of (raw) moments of random variables, hence arise often in the study of point processes and related fields.
Factorial moment measure
In probability and statistics, a factorial moment measure is a mathematical quantity, function or, more precisely, measure that is defined in relation to mathematical objects known as point processes, which are types of stochastic processes often used as mathematical models of physical phenomena representable as randomly positioned points in time, space or both. Moment measures generalize the idea of factorial moments, which are useful for studying non-negative integer-valued random variables.
Point process
In statistics and probability theory, a point process or point field is a collection of mathematical points randomly located on a mathematical space such as the real line or Euclidean space. Point processes can be used for spatial data analysis, which is of interest in such diverse disciplines as forestry, plant ecology, epidemiology, geography, seismology, materials science, astronomy, telecommunications, computational neuroscience, economics and others.
Continuum percolation theory
In mathematics and probability theory, continuum percolation theory is a branch of mathematics that extends discrete percolation theory to continuous space (often Euclidean space Rn). More specifically, the underlying points of discrete percolation form types of lattices whereas the underlying points of continuum percolation are often randomly positioned in some continuous space and form a type of point process. For each point, a random shape is frequently placed on it and the shapes overlap each with other to form clumps or components.
Point process notation
In probability and statistics, point process notation comprises the range of mathematical notation used to symbolically represent random objects known as point processes, which are used in related fields such as stochastic geometry, spatial statistics and continuum percolation theory and frequently serve as mathematical models of random phenomena, representable as points, in time, space or both. The notation varies due to the histories of certain mathematical fields and the different interpretations of point processes, and borrows notation from mathematical areas of study such as measure theory and set theory.
Point process operation
In probability and statistics, a point process operation or point process transformation is a type of mathematical operation performed on a random object known as a point process, which are often used as mathematical models of phenomena that can be represented as points randomly located in space. These operations can be purely random, deterministic or both, and are used to construct new point processes, which can be then also used as mathematical models.