For use in technical analysis of financial instruments, see Stochastic oscillator.
Randomly determined process
This article may have too many section headers. Please help consolidate the article.(January 2020) (Learn how and when to remove this template message)
Stochastic (/stəˈkæstɪk/; from Ancient Greek στόχος (stókhos) 'aim, guess')[1] refers to the property of being well-described by a random probability distribution.[1] Although stochasticity and randomness are distinct in that the former refers to a modeling approach and the latter refers to phenomena themselves, these two terms are often used synonymously. Furthermore, in probability theory, the formal concept of a stochastic process is also referred to as a random process.[2][3][4][5][6]
Stochasticity is used in many different fields, including the natural sciences such as biology,[7] chemistry,[8] ecology,[9] neuroscience,[10] and physics,[11] as well as technology and engineering fields such as image processing, signal processing,[12] information theory,[13] computer science,[14] cryptography,[15] and telecommunications.[16] It is also used in finance, due to seemingly random changes in financial markets[17][18][19] as well as in medicine, linguistics, music, media, colour theory, botany, manufacturing, and geomorphology.
^ ab"Stochastic". Lexico UK English Dictionary. Oxford University Press. Archived from the original on January 2, 2020.
^Robert J. Adler; Jonathan E. Taylor (29 January 2009). Random Fields and Geometry. Springer Science & Business Media. pp. 7–8. ISBN 978-0-387-48116-6.
^David Stirzaker (2005). Stochastic Processes and Models. Oxford University Press. p. 45. ISBN 978-0-19-856814-8.
^Loïc Chaumont; Marc Yor (19 July 2012). Exercises in Probability: A Guided Tour from Measure Theory to Random Processes, Via Conditioning. Cambridge University Press. p. 175. ISBN 978-1-107-60655-5.
^Murray Rosenblatt (1962). Random Processes. Oxford University Press. p. 91. ISBN 9780758172174.
^Olav Kallenberg (8 January 2002). Foundations of Modern Probability. Springer Science & Business Media. pp. 24 and 25. ISBN 978-0-387-95313-7.
^Paul C. Bressloff (22 August 2014). Stochastic Processes in Cell Biology. Springer. ISBN 978-3-319-08488-6.
^N.G. Van Kampen (30 August 2011). Stochastic Processes in Physics and Chemistry. Elsevier. ISBN 978-0-08-047536-3.
^Russell Lande; Steinar Engen; Bernt-Erik Sæther (2003). Stochastic Population Dynamics in Ecology and Conservation. Oxford University Press. ISBN 978-0-19-852525-7.
^Carlo Laing; Gabriel J Lord (2010). Stochastic Methods in Neuroscience. OUP Oxford. ISBN 978-0-19-923507-0.
^Wolfgang Paul; Jörg Baschnagel (11 July 2013). Stochastic Processes: From Physics to Finance. Springer Science & Business Media. ISBN 978-3-319-00327-6.
^Edward R. Dougherty (1999). Random processes for image and signal processing. SPIE Optical Engineering Press. ISBN 978-0-8194-2513-3.
^Thomas M. Cover; Joy A. Thomas (28 November 2012). Elements of Information Theory. John Wiley & Sons. p. 71. ISBN 978-1-118-58577-1.
^Michael Baron (15 September 2015). Probability and Statistics for Computer Scientists, Second Edition. CRC Press. p. 131. ISBN 978-1-4987-6060-7.
^Jonathan Katz; Yehuda Lindell (2007-08-31). Introduction to Modern Cryptography: Principles and Protocols. CRC Press. p. 26. ISBN 978-1-58488-586-3.
^François Baccelli; Bartlomiej Blaszczyszyn (2009). Stochastic Geometry and Wireless Networks. Now Publishers Inc. pp. 200–. ISBN 978-1-60198-264-3.
^J. Michael Steele (2001). Stochastic Calculus and Financial Applications. Springer Science & Business Media. ISBN 978-0-387-95016-7.
^Marek Musiela; Marek Rutkowski (21 January 2006). Martingale Methods in Financial Modelling. Springer Science & Business Media. ISBN 978-3-540-26653-2.
^Steven E. Shreve (3 June 2004). Stochastic Calculus for Finance II: Continuous-Time Models. Springer Science & Business Media. ISBN 978-0-387-40101-0.
Stochastic (/stəˈkæstɪk/; from Ancient Greek στόχος (stókhos) 'aim, guess') refers to the property of being well-described by a random probability distribution...
In probability theory and related fields, a stochastic (/stəˈkæstɪk/) or random process is a mathematical object usually defined as a sequence of random...
Stochastic terrorism initially referred to a method of mathematically predicting overall risk of a terrorist attack by using various indicators such as...
In mathematics, a stochastic matrix is a square matrix used to describe the transitions of a Markov chain. Each of its entries is a nonnegative real number...
Stochastic gradient descent (often abbreviated SGD) is an iterative method for optimizing an objective function with suitable smoothness properties (e...
In machine learning, the term stochastic parrot is a metaphor to describe the theory that large language models, though able to generate plausible language...
A stochastic differential equation (SDE) is a differential equation in which one or more of the terms is a stochastic process, resulting in a solution...
Stochastic calculus is a branch of mathematics that operates on stochastic processes. It allows a consistent theory of integration to be defined for integrals...
Stochastic optimization (SO) methods are optimization methods that generate and use random variables. For stochastic problems, the random variables appear...
In statistics, stochastic volatility models are those in which the variance of a stochastic process is itself randomly distributed. They are used in the...
Stochastic dominance is a partial order between random variables. It is a form of stochastic ordering. The concept arises in decision theory and decision...
Stochastic computing is a collection of techniques that represent continuous values by streams of random bits. Complex computations can then be computed...
In probability theory and statistics, a stochastic order quantifies the concept of one random variable being "bigger" than another. These are usually partial...
Algebra is the branch of mathematics that studies algebraic structures and the manipulation of statements within those structures. It is a generalization...
own previous values and on a stochastic term (an imperfectly predictable term); thus the model is in the form of a stochastic difference equation (or recurrence...
mathematical optimization, stochastic programming is a framework for modeling optimization problems that involve uncertainty. A stochastic program is an optimization...
Stochastic resonance (SR) is a phenomenon in which a signal that is normally too weak to be detected by a sensor can be boosted by adding white noise to...
resulting from the stochastic nature of modern computers. Unlike traditional computer forensics, which relies on digital artifacts, stochastic forensics does...
strict/strictly stationary process or strong/strongly stationary process) is a stochastic process whose unconditional joint probability distribution does not change...
Stochastic frontier analysis (SFA) is a method of economic modeling. It has its starting point in the stochastic production frontier models simultaneously...
In probability theory, stochastic drift is the change of the average value of a stochastic (random) process. A related concept is the drift rate, which...
Stochastic approximation methods are a family of iterative methods typically used for root-finding problems or for optimization problems. The recursive...
In technical analysis of securities trading, the stochastic oscillator is a momentum indicator that uses support and resistance levels. George Lane developed...
In game theory, a stochastic game (or Markov game), introduced by Lloyd Shapley in the early 1950s, is a repeated game with probabilistic transitions played...
contamination, noise pollution and over-illumination.[citation needed] A non-stochastic or deterministic health effect has a severity that is dependent on dose...
The stochastic block model is a generative model for random graphs. This model tends to produce graphs containing communities, subsets of nodes characterized...
In mathematics, especially in probability and combinatorics, a doubly stochastic matrix (also called bistochastic matrix) is a square matrix X = ( x i...
Global Information