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If a process is $\mathcal{F}_t$-progressive then it is $\mathcal{F}_t$-adapted

score 61 · Answer 1 · 2026-04-15 23:16:48

61

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If a process is $\mathcal{F}_t$-progressive then it is $\mathcal{F}_t$-adapted

Published on 15 Apr 2026 - 23:16

score 151 · Answer 2 · 2026-04-14 22:10:29

151

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score 295 · Answer 3 · 2026-05-10 21:20:37

295

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Prove $\mathbb{E}[e^{i \lambda W_t}-1] = -\frac{\lambda^2}{2} \mathbb{E}\left[ \int_0^te^{i\lambda W_s}ds\right]$, where $W_t$ is Brownian motion?

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score 76 · Answer 4 · 2026-05-11 02:50:24

76

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$M(t)=W(t)^{4} -$ $6\int_0^t W(s)^{2} \,ds$ is a martingale where $W(t)$ represents the standard Brownian Motion

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score 160 · Answer 5 · 2026-05-10 13:51:01

160

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Show that $P^0( a<W_\theta \leq b \vert W_t=y)\leq P^0( a<W_\theta \leq b \vert W_t=\frac{a+b}{2})$

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score 127 · Answer 6 · 2026-04-17 03:53:36

127

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233

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30

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199

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renewal process with underlying distribution

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score 95 · Answer 11 · 2026-04-29 12:41:35

95

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score 73 · Answer 12 · 2026-04-12 05:39:03

73

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$(X,Y)$ and $Z$ Gaussian with $Z \bot X$, $Z \bot Y$ implies $(X+Z,Y+Z)$ Gaussian

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891

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score 1.2k · Answer 15 · 2026-05-10 19:12:50

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List Question

If a process is $\mathcal{F}_t$-progressive then it is $\mathcal{F}_t$-adapted

Quick question regarding $E^Q(Y) = E^P(YZ_t)$

Prove $\mathbb{E}[e^{i \lambda W_t}-1] = -\frac{\lambda^2}{2} \mathbb{E}\left[ \int_0^te^{i\lambda W_s}ds\right]$, where $W_t$ is Brownian motion?

$M(t)=W(t)^{4} -$ $6\int_0^t W(s)^{2} \,ds$ is a martingale where $W(t)$ represents the standard Brownian Motion

Show that $P^0( a<W_\theta \leq b \vert W_t=y)\leq P^0( a<W_\theta \leq b \vert W_t=\frac{a+b}{2})$

Second derivative of $f(x)=\max(0,x-c)$

Differential of discount process

Representation of Ito integral

Is $<r_tdt,r_tdt>$ when $r_t$ stochastic?

renewal process with underlying distribution

Are local martingales semimartingales in an enlarged filtration (under particular assumption)?

$(X,Y)$ and $Z$ Gaussian with $Z \bot X$, $Z \bot Y$ implies $(X+Z,Y+Z)$ Gaussian

Geometric brownian motion with more than one brownian motion term

Rewriting sum of correlated Brownian Motions as a single brownian motion

Covariance between Wiener process and stochastic integral

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