List questions from martingales

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Prove $A_{\infty} < \infty$?

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If $M_n \to M_{\infty}$ in $\mathscr L^{2}$, then inequality holds with equality

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$P($partial sums of $\sum X_k$ are bounded$)>0 \to \sum_{k=1}^{\infty} X_k < \infty\ \text{a.s.}$

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Prove $X_{\infty} < \infty$

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Show local martingale

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$T$ can be $\infty$ with positive probability

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Convergence of $\sum_{i \leq n} X_i/n$

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Is every discrete martingale a time-changed simple random walk?

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Using the martingale central limit theorem

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non negative super martingale

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process with integral is martingale

Published on 11 May 2016 - 14:16

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Quadratic Variation of Brownian motion martingale

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Understanding the $\sigma$-algebra of a sum of random variables

Published on 11 May 2016 - 17:26

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show that the process is a martingale

Published on 11 May 2016 - 18:36

List Question

Prove $|M_{T \wedge n}| \le c + K$

Prove $A_{\infty} < \infty$?

If $M_n \to M_{\infty}$ in $\mathscr L^{2}$, then inequality holds with equality

$P($partial sums of $\sum X_k$ are bounded$)>0 \to \sum_{k=1}^{\infty} X_k < \infty\ \text{a.s.}$

Prove $X_{\infty} < \infty$

Show local martingale

$T$ can be $\infty$ with positive probability

Convergence of $\sum_{i \leq n} X_i/n$

Is every discrete martingale a time-changed simple random walk?

Using the martingale central limit theorem

non negative super martingale

process with integral is martingale

Quadratic Variation of Brownian motion martingale

Understanding the $\sigma$-algebra of a sum of random variables

show that the process is a martingale

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