# stochastic processes

Published articles for stochastic processes.

This is one page of public article previews, not the complete archive. Follow Next page to continue. Summaries are not the original full articles.

## Martingales and the Optional Stopping Theorem

DevFeed: [Martingales and the Optional Stopping Theorem](<https://devfeed.tech/articles/martingales-and-the-optional-stopping-theorem-40349.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2014/03/03/martingales-and-the-optional-stopping-theorem/>)

Published: 2014-03-03T10:00:38Z

Content type: tutorial

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [math](<https://devfeed.tech/topics/math.md>)

Tags: [2-sat](<https://devfeed.tech/tags/2-sat.md>), [conditional-probability](<https://devfeed.tech/tags/conditional-probability.md>), [expectation](<https://devfeed.tech/tags/expectation.md>), [gambling](<https://devfeed.tech/tags/gambling.md>), [martingales](<https://devfeed.tech/tags/martingales.md>), [mathematics](<https://devfeed.tech/tags/mathematics.md>), [optional-stopping-theorem](<https://devfeed.tech/tags/optional-stopping-theorem.md>), [primer](<https://devfeed.tech/tags/primer.md>), [probability-theory](<https://devfeed.tech/tags/probability-theory.md>), [random](<https://devfeed.tech/tags/random.md>), [random-variables](<https://devfeed.tech/tags/random-variables.md>), [randomized-algorithm](<https://devfeed.tech/tags/randomized-algorithm.md>), [stochastic-processes](<https://devfeed.tech/tags/stochastic-processes.md>), [theory](<https://devfeed.tech/tags/theory.md>)

### AI overview

This primer introduces martingales as models of fair betting games and explains their connection to probability theory. It begins with a geometric-distribution exercise involving repeated die throws, then introduces the ABRACADABRA problem using a monkey typing random letters.

### Source excerpt

This is a guest post by my colleague Adam Lelkes. The goal of this primer is to introduce an important and beautiful tool from probability theory, a model of fair betting games called martingales. In this post I will assume that the reader is familiar with the basics of probability theory. For those that need to refresh their knowledge, Jeremy's excellent primers (1, 2) are a good place to start.