Question

Showing a predictable gambling strategy gives a supermartingale

score 205 · Answer 1 · 2016-03-05 19:13:13

205

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Showing a predictable gambling strategy gives a supermartingale

Published on 05 Mar 2016 - 19:13

score 289 · Answer 2 · 2016-03-05 20:19:47

289

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If we have that $\tau \leq \nu$ are stopping times and that $X_n$ is a submartingale, how to show $E(X_{\tau \wedge n}) \leq E(X_{\nu \wedge n})$

Published on 05 Mar 2016 - 20:19

score 94 · Answer 3 · 2026-02-23 13:42:57

94

Views

Prove convergence of quadratic variation.

Published on 23 Feb 2026 - 13:42

score 276 · Answer 4 · 2016-03-07 00:39:12

276

Views

For Brownian Motion $B_t$, and stop time $\nu = \inf\{t: B_t = r\}$, how to show $E(e^{-\alpha\nu}) = e^{-|r|\sqrt{2\alpha}}$?

Published on 07 Mar 2016 - 0:39

score 277 · Answer 5 · 2016-03-07 01:09:26

277

Views

If $X_n, Y_n$ are martingales, $E(X^2_{n+1})-E(X^2_n) \geq \frac{[E(X_{n+1}Y_{n+1})]^2}{E(Y^2_{n+1})} - \frac{[E(X_{n}Y_{n})]^2}{E(Y^2_{n})}$

Published on 07 Mar 2016 - 1:09

score 2.7k · Answer 6 · 2016-03-07 01:38:41

2.7k

Views

If $B_t$ is standard Brownian Motion, how to show that $X_t = B_t^2-t$ is a martingale?

Published on 07 Mar 2016 - 1:38

score 277 · Answer 7 · 2026-04-03 18:13:51

277

Views

For a simple random walk $S_n$ and for a stopping time $\tau$, what is the intuitive interpretation of $P(\tau < \infty) = 1$?

Published on 03 Apr 2026 - 18:13

score 163 · Answer 8 · 2016-03-07 09:26:10

163

Views

Are there two distinctly separate definitions for the Optional Stopping Theorem?

Published on 07 Mar 2016 - 9:26

score 495 · Answer 9 · 2016-03-07 11:46:23

495

Views

Showing time inversion of a Brownian Motion $X_t = tB_{1/t}$ is continuous at $t=0$ USING the fact $X_t$ is BM on $\mathbb{Q}$?

Published on 07 Mar 2016 - 11:46

score 1.9k · Answer 10 · 2016-03-09 11:05:50

1.9k

Views

If $B_t$ is a standard brownian motion process, is $B_t^2 - \frac{t}{2}$ a martingale w.r.t. brownian motion?

Published on 09 Mar 2016 - 11:05

score 505 · Answer 11 · 2016-03-09 11:31:00

505

Views

Limit of random variables with martingale

Published on 09 Mar 2016 - 11:31

score 167 · Answer 12 · 2016-03-14 00:51:42

167

Views

If $(M_t)_{t \in [a,b]}$ is a martingale, then $t \mapsto E [ M_t ]$ is continuous.

Published on 14 Mar 2016 - 0:51

score 92 · Answer 13 · 2016-03-14 07:57:52

92

Views

Modification of a submartingale $(M_t)_{t}$ that is determined by rational limits approaching from the right

Published on 14 Mar 2016 - 7:57

score 139 · Answer 14 · 2016-03-14 14:23:24

139

Views

Martingale property for two stochastic processes

Published on 14 Mar 2016 - 14:23

score 900 · Answer 15 · 2016-03-14 22:33:27

900

Views

How does the sum of squared martingale difference sequence concentrate?

Published on 14 Mar 2016 - 22:33

List Question

Showing a predictable gambling strategy gives a supermartingale

If we have that $\tau \leq \nu$ are stopping times and that $X_n$ is a submartingale, how to show $E(X_{\tau \wedge n}) \leq E(X_{\nu \wedge n})$

Prove convergence of quadratic variation.

For Brownian Motion $B_t$, and stop time $\nu = \inf\{t: B_t = r\}$, how to show $E(e^{-\alpha\nu}) = e^{-|r|\sqrt{2\alpha}}$?

If $X_n, Y_n$ are martingales, $E(X^2_{n+1})-E(X^2_n) \geq \frac{[E(X_{n+1}Y_{n+1})]^2}{E(Y^2_{n+1})} - \frac{[E(X_{n}Y_{n})]^2}{E(Y^2_{n})}$

If $B_t$ is standard Brownian Motion, how to show that $X_t = B_t^2-t$ is a martingale?

For a simple random walk $S_n$ and for a stopping time $\tau$, what is the intuitive interpretation of $P(\tau < \infty) = 1$?

Are there two distinctly separate definitions for the Optional Stopping Theorem?

Showing time inversion of a Brownian Motion $X_t = tB_{1/t}$ is continuous at $t=0$ USING the fact $X_t$ is BM on $\mathbb{Q}$?

If $B_t$ is a standard brownian motion process, is $B_t^2 - \frac{t}{2}$ a martingale w.r.t. brownian motion?

Limit of random variables with martingale

If $(M_t)_{t \in [a,b]}$ is a martingale, then $t \mapsto E [ M_t ]$ is continuous.

Modification of a submartingale $(M_t)_{t}$ that is determined by rational limits approaching from the right

Martingale property for two stochastic processes

How does the sum of squared martingale difference sequence concentrate?

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