Question

Let $\{W_t\}_{t\geq0}$ be a Brownian motion. Define $Y_t=e^{\frac{t}{2}}\sin(W_t)$. Show that $\{Y_t\}_{t\geq0}$ is a martingale

score 254 · Answer 1 · 2026-03-24 20:33:37

254

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Let $\{W_t\}_{t\geq0}$ be a Brownian motion. Define $Y_t=e^{\frac{t}{2}}\sin(W_t)$. Show that $\{Y_t\}_{t\geq0}$ is a martingale

Published on 24 Mar 2026 - 20:33

score 521 · Answer 2 · 2026-03-25 03:06:58

521

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Finite Expected Value of Martingale

Published on 25 Mar 2026 - 3:06

score 555 · Answer 3 · 2026-03-25 19:04:50

555

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About a step in the proof of Doob's $L^{p}$-maximal inequality

Published on 25 Mar 2026 - 19:04

score 151 · Answer 4 · 2026-03-24 20:32:08

151

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For what values of $b$ is $X_{t}=e^{bt+ \sigma w_t}$ a martingale?

Published on 24 Mar 2026 - 20:32

score 101 · Answer 5 · 2026-03-17 11:53:08

101

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Expected Value of Stochastic Process, Martingale

Published on 17 Mar 2026 - 11:53

score 162 · Answer 6 · 2026-03-17 08:30:51

162

Views

Martingale Convergence Theorem rational numbers

Published on 17 Mar 2026 - 8:30

score 339 · Answer 7 · 2026-03-25 03:03:16

339

Views

Durrett: Showing $E(\log Y)$ is negative when $Y$ is nonnegative with $E(Y) = 1$ and $P(Y = 1) < 1$

Published on 25 Mar 2026 - 3:03

score 1.1k · Answer 8 · 2026-03-20 06:08:27

1.1k

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How can a martingale be a density process?

Published on 20 Mar 2026 - 6:08

score 873 · Answer 9 · 2026-03-17 09:29:30

873

Views

Applying Ito's formula on a $C^1$ only differentiable function yielding a martingale

Published on 17 Mar 2026 - 9:29

score 561 · Answer 10 · 2026-03-17 19:12:08

561

Views

How do I compute the distribution of the limit of this martingale.

Published on 17 Mar 2026 - 19:12

score 319 · Answer 11 · 2026-03-20 09:44:17

319

Views

Levy Process and characteristic function

Published on 20 Mar 2026 - 9:44

score 641 · Answer 12 · 2026-03-25 00:06:35

641

Views

American call option is a submartingale

Published on 25 Mar 2026 - 0:06

score 2.3k · Answer 13 · 2026-03-24 20:32:00

2.3k

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Martingale and Stopping Time with Finite Expectation

Published on 24 Mar 2026 - 20:32

score 105 · Answer 14 · 2018-02-11 23:15:02

105

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Show that $Z(M_{s \wedge t} - M_{r \wedge t})$ is a martingale when $M$ is a martingale and $Z \in \mathscr{F}_r$

Published on 11 Feb 2018 - 23:15

score 812 · Answer 15 · 2026-03-23 11:02:47

812

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Limit of the expectation in Galton-Watson-process using a Martingale

Published on 23 Mar 2026 - 11:02

List Question

Let $\{W_t\}_{t\geq0}$ be a Brownian motion. Define $Y_t=e^{\frac{t}{2}}\sin(W_t)$. Show that $\{Y_t\}_{t\geq0}$ is a martingale

Finite Expected Value of Martingale

About a step in the proof of Doob's $L^{p}$-maximal inequality

For what values of $b$ is $X_{t}=e^{bt+ \sigma w_t}$ a martingale?

Expected Value of Stochastic Process, Martingale

Martingale Convergence Theorem rational numbers

Durrett: Showing $E(\log Y)$ is negative when $Y$ is nonnegative with $E(Y) = 1$ and $P(Y = 1) < 1$

How can a martingale be a density process?

Applying Ito's formula on a $C^1$ only differentiable function yielding a martingale

How do I compute the distribution of the limit of this martingale.

Levy Process and characteristic function

American call option is a submartingale

Martingale and Stopping Time with Finite Expectation

Show that $Z(M_{s \wedge t} - M_{r \wedge t})$ is a martingale when $M$ is a martingale and $Z \in \mathscr{F}_r$

Limit of the expectation in Galton-Watson-process using a Martingale

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