- Martingale (probability theory) - Wikipedia
In probability theory, a martingale is a stochastic process in which the expected value of the next observation, given all prior observations, is equal to the most recent value In other words, the conditional expectation of the next value, given the past, is equal to the present value
- 17. 1: Introduction to Martingalges - Statistics LibreTexts
The term martingale originally referred to a portion of the harness of a horse, and was later used to describe gambling strategies, such as the one used in the Petersburg paradox, in which bets are doubled when a game is lost
- Martingales - Yale University
This fact is not as useful as one might think for getting bounds: given a martingale, it is almost always better to work with the martingale directly and then apply Jensen's inequality or f afterwards to get the desired bound
- Introduction to Martingales - Duke University
Informally a martingale is simply a stochastic process Mt defined on some probability space (Ω, F, P) and indexed by some ordered set T that is “con-ditionally constant,” i e , whose predicted value at any future time s > t is the same as its present value at the time t of prediction
- vol1. dvi - New York University
We can always assume that our nonnegative martingale has its expecta-tion equal to 1 because we can always multiply by a suitable constant Here is a way in which such martingales arise
- Martingale - Encyclopedia of Mathematics
One of the basic facts of the theory of martingales is that the structure of a martingale (submartingale) $ X = ( X _ {t} , {\mathcal F} _ {t} ) $ is preserved under a random change of time
- 18. 600 Probability and Random Variables F2019: Supplementary notes
In this context, the martingale condition states informally that “The expected value of the stock tomorrow, given all I know today, is the value of the stock today ”
- Martingale -- from Wolfram MathWorld
The concept of martingales is due to Lévy, and it was developed extensively by Doob A one-dimensional random walk with steps equally
|