Martingale.ie - Martingale (probability theory) - Wikipedia

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WEBIn probability theory, a martingale is a sequence of random variables (i.e., a stochastic process) for which, at a particular time, the conditional expectation of the next value in the sequence is equal to the present value, regardless of all prior values.

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Martingale (probability theory) - Wikipedia
wikipedia.org

https://en.wikipedia.org/wiki/Martingale_(probability_theory)

WEBIn probability theory, a martingale is a sequence of random variables (i.e., a stochastic process) for which, at a particular time, the conditional expectation of the next value in the sequence is equal to the present value, regardless of all prior values.

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17.1: Introduction to Martingalges - Statistics LibreTexts
libretexts.org

https://stats.libretexts.org/Bookshelves/Probability_Theory/Probability_Mathematical_Statistics_and_Stochastic_Processes_(Siegrist)/17%3A_Martingales/17.01%3A_Introduction_to_Martingalges

WEBApr 23, 2022 · The martingale in the last theorem is known as Doob's martingale and is named for Joseph Doob who did much of the pioneering work on martingales. It's also known as the Lévy martingale, named for Paul Lévy. Doob's martingale arises naturally in the statistical context of Bayesian estimation.

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Chapter 5 Martingales. - New York University
nyu.edu

https://math.nyu.edu/~varadhan/course/PROB.ch5.pdf

WEBThe theory of martingales plays a very important ans ueful role in the study of stochastic processes. A formal definition is given below. Definition 5.1. Let (Ω, F, P ) be a probability space. A martingale se-quence of length n is a chain X 1, X 2, , Xn of random variables and corre-. Each Xi is an integrable random variable which is ...

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Martingales - Yale University
yale.edu

https://www.cs.yale.edu/homes/aspnes/pinewiki/Martingales.html

WEBIf (X t,ℱ t) is a martingale and T is a stopping time for {ℱ t}, then for any n∈ℕ, E[X min(T,n)] = E[X 0]. Proof. Define Y t = <<X 0 + latex($\sum_{i=1}^{t} (X t-X t-1) [T\\le t-1]$)>>. Then (Y t,ℱ t) is a martingale since we can treat [T≤t-1] as a sequence of bets.

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Martingale - Encyclopedia of Mathematics
encyclopediaofmath.org

https://encyclopediaofmath.org/wiki/Martingale

WEBJan 9, 2024 · The notion of a martingale is one of the most important concepts in modern probability theory. It is basic in the theories of Markov processes and stochastic integrals, and is useful in many parts of analysis (convergence theorems in ergodic theory, derivatives and lifting in measure theory, inequalities in the theory of singular integrals, etc.).

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Martingales: Definitions and Examples | SpringerLink
springer.com

https://link.springer.com/chapter/10.1007/978-3-030-78939-8_10

WEBJun 9, 2021 · Martingale theory is a cornerstone to stochastic analysis and is included in this book from that perspective. This chapter introduces the theory with examples and their basic properties. For some readers this chapter may serve as a review.

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CONDITIONAL EXPECTATION AND MARTINGALES
uchicago.edu

http://galton.uchicago.edu/~lalley/Courses/385/Martingales.pdf

WEBProposition 1. The martingale difference sequence {»n} has the following properties: (a) the random variable »n is a function of Fn; and (b) for every n ‚0, (5) E(»n¯1 jFn) ˘0. Proof. This is a trivial consequence of the deﬁnition of a martingale. Corollary 1. Let {Xn} be a martingale relative to {Yn}, with martingale difference sequence {»n}. Then for every n ‚0,

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17: Martingales - Statistics LibreTexts
libretexts.org

https://stats.libretexts.org/Bookshelves/Probability_Theory/Probability_Mathematical_Statistics_and_Stochastic_Processes_(Siegrist)/17%3A_Martingales

WEB17: Martingales. Last updated. Aug 10, 2020. Page ID. 10298. Kyle Siegrist. University of Alabama in Huntsville via Random Services. Martingalges, and their cousins sub-martingales and super-martingales are real-valued stochastic processes that are abstract generalizations of fair, favorable, and unfair gambling processes.

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Advanced Chapter 6 Martingale et al. Prob 2018 - Yale …
yale.edu

http://www.stat.yale.edu/~pollard/Courses/600.spring2018/Handouts/Martingale.pdf

WEBWhat are they? The theory of martingales (and submartingales and supermartingales and other related concepts) has had a profound effect on modern probability theory. Whole branches of probability, such as stochastic calculus, rest on martingale foundations.

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Theory of Martingales | SpringerLink
springer.com

https://link.springer.com/chapter/10.1007/978-3-031-14205-5_12

WEBAug 11, 2022 · Martingales play an important role in many developments of advanced probability theory. We present here the basic convergence theorems for martingales. These results have important applications to other random processes, including random walks and branching processes. Download chapter PDF.

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