Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Lecture

Poisson Process: Probability Law

Description

This lecture covers the Poisson process in detail, focusing on the probability law and its applications in stochastic models for communications. Topics include continuous time, inter-arrival times, intensity, and arrival processes.

This video is available exclusively on Mediaspace for a restricted audience. Please log in to MediaSpace to access it if you have the necessary permissions.

Watch on Mediaspace

Official source

Related concepts (20)

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.

Compound Poisson process

A compound Poisson process is a continuous-time stochastic process with jumps. 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 where, is the counting variable of a Poisson process with rate , and are independent and identically distributed random variables, with distribution function G, which are also independent of When are non-negative integer-valued random variables, then this compound Poisson process is known as a stuttering Poisson process.

Probability theory

Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms. Typically these axioms formalise probability in terms of a probability space, which assigns a measure taking values between 0 and 1, termed the probability measure, to a set of outcomes called the sample space.

Probability

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty. The higher the probability of an event, the more likely it is that the event will occur. A simple example is the tossing of a fair (unbiased) coin.

Probability axioms

The Kolmogorov axioms are the foundations of probability theory introduced by Russian mathematician Andrey Kolmogorov in 1933. These axioms remain central and have direct contributions to mathematics, the physical sciences, and real-world probability cases. An alternative approach to formalising probability, favoured by some Bayesians, is given by Cox's theorem. The assumptions as to setting up the axioms can be summarised as follows: Let be a measure space with being the probability of some event , and .

Related lectures (33)

Simulation & Optimization: Poisson Process & Random Numbers

Explores simulation pitfalls, random numbers, discrete & continuous distributions, and Monte-Carlo integration.

Probability and Statistics: Fundamental Theorems

Explores fundamental theorems in probability and statistics, joint probability laws, and marginal distributions.

Probability and Statistics

Covers Simpson's paradox, probability distributions, and real-life examples in probability and statistics.