Question

Uniformly integrable martingale in a finite time horizon

score 842 · Answer 1 · 2026-03-25 22:10:56

842

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Uniformly integrable martingale in a finite time horizon

Published on 25 Mar 2026 - 22:10

score 142 · Answer 2 · 2026-03-27 19:08:20

142

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prove this martingale inequality

Published on 27 Mar 2026 - 19:08

score 502 · Answer 3 · 2014-12-17 22:31:43

502

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$L^p$ Martingale convergence theorem

Published on 17 Dec 2014 - 22:31

score 123 · Answer 4 · 2014-12-30 18:36:29

123

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Equality relating $L^2$ convergence and martingales

Published on 30 Dec 2014 - 18:36

score 126 · Answer 5 · 2026-03-27 16:02:27

126

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Bound on sum random variables and Martingales

Published on 27 Mar 2026 - 16:02

score 20 · Answer 6 · 2019-10-02 12:42:18

20

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If $j \leq k$ and $\tau$ a stopping time, then $E(X_{j}1_{\tau = j})\leq E(X_{k}1_{\tau = j})$

Published on 02 Oct 2019 - 12:42

score 245 · Answer 7 · 2019-10-02 16:12:42

245

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Optimizing $(X_{n}+c)^{2}$ to show that $P(\overline{X}_{n}\geq \lambda) \leq E(X_{n}^{2})/(EX_{n}^{2}+ \lambda^{2})$

Published on 02 Oct 2019 - 16:12

score 56 · Answer 8 · 2019-10-02 19:19:43

56

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Let $\xi_{n}=X_{n}-X_{n-1}$ where $EX_{0}^{2}, \sum\limits_{m}E\xi_{m}^{2} < \infty$ then $X_{n} \to X_{\infty}-$a.s. and $L^{2}$

Published on 02 Oct 2019 - 19:19

score 30 · Answer 9 · 2019-10-04 08:22:36

30

Views

Showing that $M_{\tau}$ and $M_{\tau \land n}$ are integrable

Published on 04 Oct 2019 - 8:22

score 118 · Answer 10 · 2019-10-04 22:30:52

118

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Show that $P(\lim\limits_{n\to \infty} X_{n}=0 \operatorname{or} 1)=1$ and if $X_{0}=\theta$ then $P(\lim\limits_{n\to \infty} X_{n}=1)=\theta$

Published on 04 Oct 2019 - 22:30

score 45 · Answer 11 · 2026-03-26 14:34:33

45

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How can I justify $E[X_{\tau}]\leq E[X_{0}]=1$ If I cannot show $\tau \leq c$ a.s.

Published on 26 Mar 2026 - 14:34

score 76 · Answer 12 · 2019-10-06 01:25:34

76

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Controlling extreme values without Doob's maximal inequality?

Published on 06 Oct 2019 - 1:25

score 158 · Answer 13 · 2019-10-06 21:29:45

158

Views

Calculating $P(S_\tau = b)$ where $S_n$ is the symmetric random walk

Published on 06 Oct 2019 - 21:29

score 324 · Answer 14 · 2019-10-07 15:13:48

324

Views

Verify that $\exp(-2aX_t)$ is a martingale.

Published on 07 Oct 2019 - 15:13

score 71 · Answer 15 · 2026-03-25 19:05:20

71

Views

A conceptual understanding of Filtrations and Martingales

Published on 25 Mar 2026 - 19:05

List Question

Uniformly integrable martingale in a finite time horizon

prove this martingale inequality

$L^p$ Martingale convergence theorem

Equality relating $L^2$ convergence and martingales

Bound on sum random variables and Martingales

If $j \leq k$ and $\tau$ a stopping time, then $E(X_{j}1_{\tau = j})\leq E(X_{k}1_{\tau = j})$

Optimizing $(X_{n}+c)^{2}$ to show that $P(\overline{X}_{n}\geq \lambda) \leq E(X_{n}^{2})/(EX_{n}^{2}+ \lambda^{2})$

Let $\xi_{n}=X_{n}-X_{n-1}$ where $EX_{0}^{2}, \sum\limits_{m}E\xi_{m}^{2} < \infty$ then $X_{n} \to X_{\infty}-$a.s. and $L^{2}$

Showing that $M_{\tau}$ and $M_{\tau \land n}$ are integrable

Show that $P(\lim\limits_{n\to \infty} X_{n}=0 \operatorname{or} 1)=1$ and if $X_{0}=\theta$ then $P(\lim\limits_{n\to \infty} X_{n}=1)=\theta$

How can I justify $E[X_{\tau}]\leq E[X_{0}]=1$ If I cannot show $\tau \leq c$ a.s.

Controlling extreme values without Doob's maximal inequality?

Calculating $P(S_\tau = b)$ where $S_n$ is the symmetric random walk

Verify that $\exp(-2aX_t)$ is a martingale.

A conceptual understanding of Filtrations and Martingales

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