# Questions tagged [martingale]

In probability theory, a martingale is a model of a fair game where knowledge of past events never helps predict the mean of the future winnings and only the current event matters.

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### How to approach Basketball “Beat the Pro” drill with Markov Chain

Suppose, similarly to Gambler's ruin problem a Basketball player is doing "Beat the Pro" drill. That is, for every shot made, he scores one point, and for those missed, two points are to be deducted. ...
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### Upper bound for randomly weighted sum of independent random variables

I have a sequence of independent random variables {$\epsilon_j$} with mean 0. I also have another sequence of Bernoulli random variables $\delta_1, \delta_2,\dots$ which are dependent on the previous ...
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### $M_t$ Local Martingale if and only if satisfies $\frac{\partial f}{\partial t}+\frac{1}{2}\frac{\partial^2 f}{\partial x^2}=0$ proof?
I was reading the wikipedia article on local martingales and it states the following theorem Let $W_t$ be standard Brownian motion and let $f:[0,\infty)\times\mathbb{R}\rightarrow\mathbb{R}$ such ...