Question

If $E(X_n^2)<\infty$, then for a Martingale $E(X_n^2)<M$ iff $\sum_{n=1}^\infty E[(X_n-X_{n-1})^2]<\infty$

score 221 · Answer 1 · 2026-03-25 11:24:07

221

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If $E(X_n^2)<\infty$, then for a Martingale $E(X_n^2)<M$ iff $\sum_{n=1}^\infty E[(X_n-X_{n-1})^2]<\infty$

Published on 25 Mar 2026 - 11:24

score 141 · Answer 2 · 2026-03-26 14:19:55

141

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Show that this processes are martingales

Published on 26 Mar 2026 - 14:19

score 21 · Answer 3 · 2026-03-23 00:19:23

21

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Prove that a process (given through rsdes) is a martingale.

Published on 23 Mar 2026 - 0:19

score 711 · Answer 4 · 2026-03-25 12:49:46

711

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If $\tau=\inf \{t \ge 0: B(t)= -a \text{ or } b\}$ is a stopping time of Brownian motion $B_t$, why does $E(\tau)=E(B_{\tau}^2)$?

Published on 25 Mar 2026 - 12:49

score 116 · Answer 5 · 2026-03-27 00:22:51

116

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Sum of variables of a martingale

Published on 27 Mar 2026 - 0:22

score 58 · Answer 6 · 2018-12-16 18:39:26

58

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Expectation conditioned on a $\sigma$-algebra? (Martingale definition)

Published on 16 Dec 2018 - 18:39

score 674 · Answer 7 · 2018-12-17 19:01:35

674

Views

Is the sigma algebra generated by $X$ random variable and its square equal to the sigma algebra generated by $X$ alone?

Published on 17 Dec 2018 - 19:01

score 223 · Answer 8 · 2026-03-26 06:29:11

223

Views

Show that a symmetric random walk with hit any number with probability 1

Published on 26 Mar 2026 - 6:29

score 101 · Answer 9 · 2026-03-26 16:03:59

101

Views

Integrability in Dynkin's formula

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score 242 · Answer 10 · 2018-12-27 05:26:11

242

Views

question about martingale about maximal inequality for submartigales

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score 1.3k · Answer 11 · 2026-03-25 16:02:33

1.3k

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The distribution of a stopping time

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score 1.2k · Answer 12 · 2026-03-25 12:48:42

1.2k

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Show a Continuous Local Martingale is a Martingale

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score 912 · Answer 13 · 2026-03-25 15:59:02

912

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Is Conditional Expectation of stochastic process a martingale?

Published on 25 Mar 2026 - 15:59

score 722 · Answer 14 · 2026-03-25 16:12:41

722

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A martingale that does not converge in $L^1$

Published on 25 Mar 2026 - 16:12

score 90 · Answer 15 · 2026-03-25 14:26:58

90

Views

Compute $E(M_σ)$ when $σ = \inf(t ≥ 0: |B_t| = 1)$ and $M_t = 4B^2_t +e^{4B_t−8t}−4t$

Published on 25 Mar 2026 - 14:26

List Question

If $E(X_n^2)<\infty$, then for a Martingale $E(X_n^2)<M$ iff $\sum_{n=1}^\infty E[(X_n-X_{n-1})^2]<\infty$

Show that this processes are martingales

Prove that a process (given through rsdes) is a martingale.

If $\tau=\inf \{t \ge 0: B(t)= -a \text{ or } b\}$ is a stopping time of Brownian motion $B_t$, why does $E(\tau)=E(B_{\tau}^2)$?

Sum of variables of a martingale

Expectation conditioned on a $\sigma$-algebra? (Martingale definition)

Is the sigma algebra generated by $X$ random variable and its square equal to the sigma algebra generated by $X$ alone?

Show that a symmetric random walk with hit any number with probability 1

Integrability in Dynkin's formula

question about martingale about maximal inequality for submartigales

The distribution of a stopping time

Show a Continuous Local Martingale is a Martingale

Is Conditional Expectation of stochastic process a martingale?

A martingale that does not converge in $L^1$

Compute $E(M_σ)$ when $σ = \inf(t ≥ 0: |B_t| = 1)$ and $M_t = 4B^2_t +e^{4B_t−8t}−4t$

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