Search results
Results from the WOW.Com Content Network
A visual depiction of a Poisson point process starting. In probability theory, statistics and related fields, a Poisson point process (also known as: Poisson random measure, Poisson random point field and Poisson point field) is a type of mathematical object that consists of points randomly located on a mathematical space with the essential feature that the points occur independently of one ...
A Poisson (counting) process on the line can be characterised by two properties : the number of points (or events) in disjoint intervals are independent and have a Poisson distribution. A Poisson point process can also be defined using these two properties. Namely, we say that a point process is a Poisson point process if the following two ...
The renewal process is a generalization of the Poisson process. In essence, the Poisson process is a continuous-time Markov process on the positive integers (usually starting at zero) which has independent exponentially distributed holding times at each integer i {\displaystyle i} before advancing to the next integer, i + 1 {\displaystyle i+1} .
An important point about infinitely divisible distributions is their connection to Lévy processes, i.e. at any point in time a Lévy process is infinitely divisibly distributed. Many families of well-known infinitely divisible distributions are so-called convolution-closed, i.e. if the distribution of a Lévy process at one point in time ...
In probability theory and statistics, Campbell's theorem or the Campbell–Hardy theorem is either a particular equation or set of results relating to the expectation of a function summed over a point process to an integral involving the mean measure of the point process, which allows for the calculation of expected value and variance of the random sum.
The jumps arrive randomly according to a Poisson process and the size of the jumps is also random, with a specified probability distribution. To be precise, a compound Poisson process, parameterised by a rate > and jump size distribution G, is a process {():} given by
The process is named after the statistician David Cox, who first published the model in 1955. [ 1 ] Cox processes are used to generate simulations of spike trains (the sequence of action potentials generated by a neuron ), [ 2 ] and also in financial mathematics where they produce a "useful framework for modeling prices of financial instruments ...
In queueing theory, a discipline within the mathematical theory of probability, a Markovian arrival process (MAP or MArP [1]) is a mathematical model for the time between job arrivals to a system. The simplest such process is a Poisson process where the time between each arrival is exponentially distributed. [2] [3]