List questions from martingales

Published on 12 Dec 2013 - 22:06

145

Views

How $\Pi_{i=0}^n\xi_i$ converges a.s. to $0$ provided $\xi_n>0 $, iid and $E(\xi_n)=1$

Published on 14 Dec 2013 - 8:00

441

Views

Example of a sequence of r.v.'s with constant stopping time that is not a Martingale

Published on 14 Dec 2013 - 17:54

587

Views

Prove $Y_n:=\sup|\hat{F}_n(x)-F(x)|$ is a reverse submartingale

Published on 16 Dec 2013 - 3:30

603

Views

Karatzas and Shreve Problem 3.3.38

Published on 17 Dec 2013 - 11:43

136

Views

Conditions for Martingale

Published on 18 Dec 2013 - 6:37

815

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Time scaling of Brownian motion

Published on 19 Dec 2013 - 2:31

422

Views

Show the following is Local Martingale

Published on 19 Dec 2013 - 3:13

1k

Views

Can you make money on coin tosses when the odds are against you?

Published on 26 Mar 2026 - 22:58

433

Views

Fake Brownian Motion

Published on 19 Dec 2013 - 9:12

234

Views

Hoeffding-type bound covering all partial sums? (better than naive union bound)

Published on 20 Dec 2013 - 6:40

335

Views

Expectation of (super/sub)-martingales

Published on 29 Dec 2013 - 14:32

679

Views

Absolute continuity of quadratic variation of continuous local martingales

Published on 23 Feb 2026 - 15:18

836

Views

Convergence of a conditional expectation

Published on 02 Jan 2014 - 21:00

184

Views

Azuma's inequality: Expected sum of differences

Published on 29 Mar 2026 - 5:34

List Question

Variance With Martingales Problem - Answered; Ignore the Bounty

How $\Pi_{i=0}^n\xi_i$ converges a.s. to $0$ provided $\xi_n>0 $, iid and $E(\xi_n)=1$

Example of a sequence of r.v.'s with constant stopping time that is not a Martingale

Prove $Y_n:=\sup|\hat{F}_n(x)-F(x)|$ is a reverse submartingale

Karatzas and Shreve Problem 3.3.38

Conditions for Martingale

Time scaling of Brownian motion

Show the following is Local Martingale

Can you make money on coin tosses when the odds are against you?

Fake Brownian Motion

Hoeffding-type bound covering all partial sums? (better than naive union bound)

Expectation of (super/sub)-martingales

Absolute continuity of quadratic variation of continuous local martingales

Convergence of a conditional expectation

Azuma's inequality: Expected sum of differences

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