Question

Change of measure defined by Radon-Nikodym derivative

score 130 · Answer 1 · 2026-04-12 15:22:28

130

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Change of measure defined by Radon-Nikodym derivative

Published on 12 Apr 2026 - 15:22

score 237 · Answer 2 · 2026-04-07 04:47:36

237

Views

Showing an equivalence between the martingale property and a markov property.

Published on 07 Apr 2026 - 4:47

score 87 · Answer 3 · 2021-12-09 17:48:35

87

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Show that $\sum_{k=1}^n\frac{1}{k}(M_k-M_{k-1})$ is a martingale

Published on 09 Dec 2021 - 17:48

score 106 · Answer 4 · 2021-12-10 20:21:15

106

Views

Convergent hyperbolic cosine martingale $X_n = \frac{\text{exp} \big (\sum_{j=1}^n a_j Y_j \big )}{\prod_{j=1}^n \text{cosh}(a_j)}$, $Y_n$ Rademacher

Published on 10 Dec 2021 - 20:21

score 114 · Answer 5 · 2026-04-03 12:26:31

114

Views

Is it true $P(\sup_{k \in \mathbb{N}}X_k \geq \epsilon +x)=\dfrac{x}{\epsilon+x}$?

Published on 03 Apr 2026 - 12:26

score 78 · Answer 6 · 2026-04-11 06:45:02

78

Views

Maybe a Monty Hall kind of problem?

Published on 11 Apr 2026 - 6:45

score 185 · Answer 7 · 2026-04-12 14:12:51

185

Views

Proof of a maximal inequality

Published on 12 Apr 2026 - 14:12

score 168 · Answer 8 · 2026-04-06 15:58:36

168

Views

$X(n)=2^{n}(1-Y(n))$ is a martingale?

Published on 06 Apr 2026 - 15:58

score 226 · Answer 9 · 2026-04-02 15:15:04

226

Views

Example of a discrete-time martingale with uncorrelated, but dependent, increments

Published on 02 Apr 2026 - 15:15

score 70 · Answer 10 · 2026-04-13 12:59:22

70

Views

Existence of a filtration with respect to which a sequence becomes a martingale difference.

Published on 13 Apr 2026 - 12:59

score 250 · Answer 11 · 2026-04-11 23:28:00

250

Views

Limit of expectations on increasing sigma algebra converge to expectation on limit sigma algebra

Published on 11 Apr 2026 - 23:28

score 864 · Answer 12 · 2026-04-10 20:07:02

864

Views

Distribution of stopping time for biased random walk using martingales.

Published on 10 Apr 2026 - 20:07

score 54 · Answer 13 · 2021-12-22 15:17:55

54

Views

Given martingale $M$, $Y:=\mathcal{E}(X)$, does $\langle M,X \rangle = Y^{-1} \langle M,Y\rangle$ hold?

Published on 22 Dec 2021 - 15:17

score 60 · Answer 14 · 2026-04-12 00:48:28

60

Views

Is a càdlàg martingale on a finite time horizon square-integrable?

Published on 12 Apr 2026 - 0:48

score 220 · Answer 15 · 2021-12-24 16:30:59

220

Views

Show that $M_{n}=\left(\cfrac{N}{N-1}\right)^n X_n(N-X_n)$ is a martingale

Published on 24 Dec 2021 - 16:30

List Question

Change of measure defined by Radon-Nikodym derivative

Showing an equivalence between the martingale property and a markov property.

Show that $\sum_{k=1}^n\frac{1}{k}(M_k-M_{k-1})$ is a martingale

Convergent hyperbolic cosine martingale $X_n = \frac{\text{exp} \big (\sum_{j=1}^n a_j Y_j \big )}{\prod_{j=1}^n \text{cosh}(a_j)}$, $Y_n$ Rademacher

Is it true $P(\sup_{k \in \mathbb{N}}X_k \geq \epsilon +x)=\dfrac{x}{\epsilon+x}$?

Maybe a Monty Hall kind of problem?

Proof of a maximal inequality

$X(n)=2^{n}(1-Y(n))$ is a martingale?

Example of a discrete-time martingale with uncorrelated, but dependent, increments

Existence of a filtration with respect to which a sequence becomes a martingale difference.

Limit of expectations on increasing sigma algebra converge to expectation on limit sigma algebra

Distribution of stopping time for biased random walk using martingales.

Given martingale $M$, $Y:=\mathcal{E}(X)$, does $\langle M,X \rangle = Y^{-1} \langle M,Y\rangle$ hold?

Is a càdlàg martingale on a finite time horizon square-integrable?

Show that $M_{n}=\left(\cfrac{N}{N-1}\right)^n X_n(N-X_n)$ is a martingale

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