Stochastic process | Wikipedia audio article
Channel: wikipedia tts
Date: 2019-05-07

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Stochastic_process


00:03:32 1 Introduction
00:04:52 1.1 Classifications
00:06:57 1.2 Etymology
00:09:06 1.3 Terminology
00:10:35 1.4 Notation
00:12:56 2 Examples
00:13:06 2.1 Bernoulli process
00:14:13 2.2 Random walk
00:16:06 2.3 Wiener process
00:18:52 2.4 Poisson process
00:21:43 2.5 Further examples
00:21:52 2.5.1 Markov processes and chains
00:24:17 2.5.2 Martingale
00:27:58 2.5.3 Lévy process
00:30:51 2.5.4 Random field
00:31:46 2.5.5 Point process
00:33:16 3 Definitions
00:33:24 3.1 Stochastic process
00:37:55 3.2 Index set
00:39:20 3.3 State space
00:40:04 3.4 Sample function
00:42:17 3.5 Increment
00:45:01 3.6 Further definitions
00:45:11 3.6.1 Law
00:49:03 3.6.2 Finite-dimensional probability distributions
00:53:06 3.6.3 Stationarity
00:57:22 3.6.4 Filtration
01:00:34 3.6.5 Modification
01:03:23 3.6.6 Indistinguishable
01:05:15 3.6.7 Separability
01:09:34 3.6.8 Independence
01:11:29 3.6.9 Uncorrelatedness
01:14:08 3.6.10 Independence implies uncorrelatedness
01:14:35 3.6.11 Orthogonality
01:16:47 3.6.12 Skorokhod space
01:19:07 3.6.13 Regularity
01:19:44 4 History
01:19:52 4.1 Early probability theory
01:21:23 4.2 Statistical mechanics
01:22:36 4.3 Measure theory and probability theory
01:24:08 4.4 Birth of modern probability theory
01:25:31 4.5 Stochastic processes after World War II
01:28:44 4.6 Discoveries of specific stochastic processes
01:29:22 4.6.1 Bernoulli process
01:30:04 4.6.2 Random walks
01:31:38 4.6.3 Wiener process
01:34:30 4.6.4 Poisson process
01:36:30 4.6.5 Markov processes
01:39:24 4.6.6 Lévy processes
01:40:23 5 Mathematical construction
01:41:35 5.1 Construction issues
01:44:13 5.2 Resolving construction issues
01:46:13 6 See also



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SUMMARY
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In probability theory and related fields, a stochastic or random process is a mathematical object usually defined as a collection of random variables. Historically, the random variables were associated with or indexed by a set of numbers, usually viewed as points in time, giving the interpretation of a stochastic process representing numerical values of some system randomly changing over time, such as the growth of a bacterial population, an electrical current fluctuating due to thermal noise, or the movement of a gas molecule. Stochastic processes are widely used as mathematical models of systems and phenomena that appear to vary in a random manner. They have applications in many disciplines including sciences such as biology, chemistry, ecology, neuroscience, and physics as well as technology and engineering fields such as image processing, signal processing, information theory, computer science, cryptography and telecommunications. Furthermore, seemingly random changes in financial markets have motivated the extensive use of stochastic processes in finance.Applications and the study of phenomena have in turn inspired the proposal of new stochastic processes. Examples of such stochastic processes include the Wiener process or Brownian motion process, used by Louis Bachelier to study price changes on the Paris Bourse, and the Poisson process, used by A. K. Erlang to study the number of phone calls occurring in a certain period of time. These two stochastic processes are considered the most important and central in the theory of stochastic processes, and were discovered repeatedly and independently, both before and after Bachelier and Erlang, in different settings and countries.The term random function is also used to refer to a stochastic or random process, because a stochastic process can also be interpreted as a random element in a function space. The terms stochastic process and random process are used interchangeably, often with no specific mathematical space for the set that indexes the random variables. But often these t ...