Question

Does the Martingale Representation theorem hold both ways?

score 209 · Answer 1 · 2020-06-04 14:51:18

209

Views

Does the Martingale Representation theorem hold both ways?

Published on 04 Jun 2020 - 14:51

score 180 · Answer 2 · 2020-06-09 10:56:31

180

Views

Describe all martingales $(X_n)_{n\in\mathbb{N}}$, such that $X_n\in\{-1,0,1\}$ for all $n\in\mathbb{N}$ with an arbitrary sample space $\Omega$.

Published on 09 Jun 2020 - 10:56

score 128 · Answer 3 · 2026-03-25 04:41:17

128

Views

$R$ be a Noetherian semi local ring such that $R/N(R)$ is complete $\mathrm{Jac}(R)$-adically, then $R$ is complete $\mathrm{Jac}(R)$-adically.

Published on 25 Mar 2026 - 4:41

score 105 · Answer 4 · 2020-06-17 15:44:10

105

Views

Find $a_n$ and $b_n$, such that $M_n=a_nY_n+b_n$ defines a Martingale, when $E[Y_{n+1}|F_n]=u_nY_n+v_n$.

Published on 17 Jun 2020 - 15:44

score 104 · Answer 5 · 2020-06-18 16:55:29

104

Views

Shifting balls in urns that are already occupied by balls

Published on 18 Jun 2020 - 16:55

score 730 · Answer 6 · 2020-06-27 09:03:57

730

Views

A counterxample of a non-adapted process?

Published on 27 Jun 2020 - 9:03

score 88 · Answer 7 · 2020-06-30 16:36:15

88

Views

Clarification and Proof of 'equivalence' asserted in Matsumura

Published on 30 Jun 2020 - 16:36

score 128 · Answer 8 · 2020-07-09 03:03:30

128

Views

Questions about proving the statement: $\tau(\omega)$ is a stopping time, iff $\{ \tau(\omega) < t\}$ $\in \mathcal{F}_t$, for all $t \geq 0$.

Published on 09 Jul 2020 - 3:03

score 42 · Answer 9 · 2020-07-09 07:36:42

42

Views

Is the filtration of a process "evaluated" at a random time a sigma-algebra?

Published on 09 Jul 2020 - 7:36

score 102 · Answer 10 · 2020-07-29 06:47:04

102

Views

The canonical filtration of a Brownian motion is not a subset of the canonical filtration of its absolute process

Published on 29 Jul 2020 - 6:47

score 2.7k · Answer 11 · 2016-07-14 14:50:28

2.7k

Views

What is the intuition behind right-continuous filtration?

Published on 14 Jul 2016 - 14:50

score 70 · Answer 12 · 2026-03-25 11:12:39

70

Views

Counit for the filtration adjunction

Published on 25 Mar 2026 - 11:12

score 314 · Answer 13 · 2016-07-30 11:00:53

314

Views

union of natural filtration vs union of right continuous filtration

Published on 30 Jul 2016 - 11:00

score 206 · Answer 14 · 2016-08-02 07:30:54

206

Views

If $X$ is a Lévy process w.r.t. the natural filtration $\mathcal{F}$, is it so w.r.t. the right-continuous modified filtration $\mathcal{F}^+$?

Published on 02 Aug 2016 - 7:30

score 39 · Answer 15 · 2016-08-24 15:20:24

39

Views

generalized filtration with limited information

Published on 24 Aug 2016 - 15:20

List Question

Does the Martingale Representation theorem hold both ways?

Describe all martingales $(X_n)_{n\in\mathbb{N}}$, such that $X_n\in\{-1,0,1\}$ for all $n\in\mathbb{N}$ with an arbitrary sample space $\Omega$.

$R$ be a Noetherian semi local ring such that $R/N(R)$ is complete $\mathrm{Jac}(R)$-adically, then $R$ is complete $\mathrm{Jac}(R)$-adically.

Find $a_n$ and $b_n$, such that $M_n=a_nY_n+b_n$ defines a Martingale, when $E[Y_{n+1}|F_n]=u_nY_n+v_n$.

Shifting balls in urns that are already occupied by balls

A counterxample of a non-adapted process?

Clarification and Proof of 'equivalence' asserted in Matsumura

Questions about proving the statement: $\tau(\omega)$ is a stopping time, iff $\{ \tau(\omega) < t\}$ $\in \mathcal{F}_t$, for all $t \geq 0$.

Is the filtration of a process "evaluated" at a random time a sigma-algebra?

The canonical filtration of a Brownian motion is not a subset of the canonical filtration of its absolute process

What is the intuition behind right-continuous filtration?

Counit for the filtration adjunction

union of natural filtration vs union of right continuous filtration

If $X$ is a Lévy process w.r.t. the natural filtration $\mathcal{F}$, is it so w.r.t. the right-continuous modified filtration $\mathcal{F}^+$?

generalized filtration with limited information

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