# Questions tagged [martingales]

For question about discrete or continuous (super/sub)martingales. Often used with [probability-theory] tag.

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### Semi-group property of branching processes?

See the edit below! I do have a question about continuous-state branching processes while reading "Fluctuations of Lévy Processes with Applications" by Kyprianou: Let $Y$ be a continuous-...
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### Almost sure convergence of a martingale

Let $X_1,X_2,\ldots$ be i.i.d random variables with standard normal distribution $\mathcal{N}(0,1)$. We define $$N_n = e^{n/2}\sin{(X_1+X_2+\ldots X_n)}$$ and after some calculations, it's easy to ...
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### Azuma's inequality for a simple case of Polya's urn

Suppose that an urn contains one red ball and one blue ball. A ball is drawn from the urn uniformly at random. After that, the ball is put back into the urn and another ball of the same colour is ...
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### Comparing the inequalities of Azuma and Chernoff

Let $n$ be a positive integer and let $p = p(n) \in (0, 1)$. Let $X$ be the sum of the i.i.d. random variables $Y_1,\ldots, Y_n$, which are $1$ with probability $p$ and $0$ with probability $1-p$. ...
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### Computing covariation of Brownian motion and bounded variation process

Suppose $(B_t)_{t\geq0}$ is a Brownian motion and $(A_t)_{t\geq0}$ is a continuous process of bounded variation. I wish to show that $\langle A,B\rangle =0$. For this, I know that $(B_t-t)_{t\geq0}$ ...
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Given two random variables, the conditional expectation $E(Y|X)$ is a $\sigma(X)$ measurable random variable whose integration over any set in $\sigma(X)$ agrees with the integration of $Y$ over the ...