Question

Prove that the discrete time martingale can be represented by $E (Y_{n +1} \mid F_n) = 0$ if $Y_{n +1} = X_{n +1}-X_n$, for $n = 0,1, \ldots $

score 289 · Answer 1 · 2014-08-01 03:51:53

289

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Prove that the discrete time martingale can be represented by $E (Y_{n +1} \mid F_n) = 0$ if $Y_{n +1} = X_{n +1}-X_n$, for $n = 0,1, \ldots $

Published on 01 Aug 2014 - 3:51

score 1.2k · Answer 2 · 2026-03-26 08:14:49

1.2k

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A martingale with bounded increments either converges or diverges to both infinities a.s.

Published on 26 Mar 2026 - 8:14

score 2.3k · Answer 3 · 2014-08-03 03:35:38

2.3k

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Writing a martingale as the difference of two non-negative martingales

Published on 03 Aug 2014 - 3:35

score 439 · Answer 4 · 2026-02-23 08:38:22

439

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Occupancy distribution bounds for $k$ balls in $m$ bins

Published on 23 Feb 2026 - 8:38

score 152 · Answer 5 · 2014-08-09 11:18:20

152

Views

On the conditional expectation.

Published on 09 Aug 2014 - 11:18

score 46 · Answer 6 · 2014-08-11 09:44:16

46

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Is $Q_n(A_n)=E(L_n A_n)$ a probability measure?

Published on 11 Aug 2014 - 9:44

score 234 · Answer 7 · 2014-08-13 03:53:55

234

Views

Suitable martingales and optional stopping theorem

Published on 13 Aug 2014 - 3:53

score 2.5k · Answer 8 · 2014-08-13 09:09:03

2.5k

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Filtration and measure change

Published on 13 Aug 2014 - 9:09

score 38 · Answer 9 · 2014-08-17 14:44:50

38

Views

If a random integral has moments of all orders, is the same true for its kernel?

Published on 17 Aug 2014 - 14:44

score 909 · Answer 10 · 2026-03-27 10:45:41

909

Views

Stochastic integration by parts formula to prove identity between iterated integrals

Published on 27 Mar 2026 - 10:45

score 324 · Answer 11 · 2026-03-27 07:49:21

324

Views

Is there a Burkholder-Davis-Gundy inequality for martingale increments?

Published on 27 Mar 2026 - 7:49

score 69 · Answer 12 · 2026-03-26 08:15:07

69

Views

Do we need $\tau \leq \nu$ to show $E(X_\tau)=E(X_\nu)$?

Published on 26 Mar 2026 - 8:15

score 129 · Answer 13 · 2014-08-23 10:51:47

129

Views

$E[M_t|H_t]$ is a martingale with respect to $H=(H_t)_{t\geq 0}$, $H_t \subset \mathcal{F}_t \forall t$

Published on 23 Aug 2014 - 10:51

score 1k · Answer 14 · 2026-03-29 10:46:49

1k

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Centered independent increments process is a martingale

Published on 29 Mar 2026 - 10:46

score 1.7k · Answer 15 · 2014-08-25 05:44:27

1.7k

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Let $X$ be the value of the first die and $Y$ the sum of the two dice. Find $E(X / Y)$

Published on 25 Aug 2014 - 5:44

List Question

Prove that the discrete time martingale can be represented by $E (Y_{n +1} \mid F_n) = 0$ if $Y_{n +1} = X_{n +1}-X_n$, for $n = 0,1, \ldots $

A martingale with bounded increments either converges or diverges to both infinities a.s.

Writing a martingale as the difference of two non-negative martingales

Occupancy distribution bounds for $k$ balls in $m$ bins

On the conditional expectation.

Is $Q_n(A_n)=E(L_n A_n)$ a probability measure?

Suitable martingales and optional stopping theorem

Filtration and measure change

If a random integral has moments of all orders, is the same true for its kernel?

Stochastic integration by parts formula to prove identity between iterated integrals

Is there a Burkholder-Davis-Gundy inequality for martingale increments?

Do we need $\tau \leq \nu$ to show $E(X_\tau)=E(X_\nu)$?

$E[M_t|H_t]$ is a martingale with respect to $H=(H_t)_{t\geq 0}$, $H_t \subset \mathcal{F}_t \forall t$

Centered independent increments process is a martingale

Let $X$ be the value of the first die and $Y$ the sum of the two dice. Find $E(X / Y)$

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