Conditional Expectation $E[X_n|mathcal{G}]$. [on hold]
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If $x_n leq y in L^1$ and $x_n$ a.s to $x$, then show that $E[X_n|mathcal{G}]$ a.s to $E[X|mathcal{G}]$. We may need to apply Dominated Convergent Theorem.
probability-theory conditional-expectation
edited Nov 13 at 10:07
MathOverview
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asked Nov 13 at 10:03
Emilia78
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put on hold as off-topic by user10354138, saz, Davide Giraudo, Cesareo, Alexander Gruber♦ 2 days ago
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – user10354138, saz, Davide Giraudo, Cesareo, Alexander Gruber
If this question can be reworded to fit the rules in the help center, please edit the question.
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If $x_n leq y in L^1$ and $x_n$ a.s to $x$, then show that $E[X_n|mathcal{G}]$ a.s to $E[X|mathcal{G}]$. We may need to apply Dominated Convergent Theorem.
probability-theory conditional-expectation
edited Nov 13 at 10:07
MathOverview
8,52443063
asked Nov 13 at 10:03
Emilia78
11
New contributor
Emilia78 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
put on hold as off-topic by user10354138, saz, Davide Giraudo, Cesareo, Alexander Gruber♦ 2 days ago
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – user10354138, saz, Davide Giraudo, Cesareo, Alexander Gruber
If this question can be reworded to fit the rules in the help center, please edit the question.
2
Welcome to MSE. It will be more likely that you will get an answer if you show us that you made an effort. This should be added to the question rather than in the comments.
– José Carlos Santos
Nov 13 at 10:08
Consider formatting your question clearly by putting the math parts enclosed in $ .
– Gautam Shenoy
Nov 13 at 10:09
It would be easy if it was true that whenever $E[1_BY_n] rightarrow 0 $ for every set $B in mathcal{G}$, than $Y_n rightarrow 0$ a.s. . , but I do not know if this is true... Is somebody can point a reference of such a result I can write the simple reasonings...
– Thomas
Nov 13 at 17:46
add a comment |
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up vote
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If $x_n leq y in L^1$ and $x_n$ a.s to $x$, then show that $E[X_n|mathcal{G}]$ a.s to $E[X|mathcal{G}]$. We may need to apply Dominated Convergent Theorem.
probability-theory conditional-expectation
edited Nov 13 at 10:07
MathOverview
8,52443063
asked Nov 13 at 10:03
Emilia78
11
New contributor
Emilia78 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
If $x_n leq y in L^1$ and $x_n$ a.s to $x$, then show that $E[X_n|mathcal{G}]$ a.s to $E[X|mathcal{G}]$. We may need to apply Dominated Convergent Theorem.
probability-theory conditional-expectation
probability-theory conditional-expectation
edited Nov 13 at 10:07
MathOverview
8,52443063
asked Nov 13 at 10:03
Emilia78
11
New contributor
Emilia78 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited Nov 13 at 10:07
MathOverview
8,52443063
asked Nov 13 at 10:03
Emilia78
11
New contributor
Emilia78 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited Nov 13 at 10:07
MathOverview
8,52443063
edited Nov 13 at 10:07
MathOverview
8,52443063
edited Nov 13 at 10:07
MathOverview
8,52443063
8,52443063
asked Nov 13 at 10:03
Emilia78
11
New contributor
Emilia78 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Nov 13 at 10:03
Emilia78
11
asked Nov 13 at 10:03
Emilia78
11
11
New contributor
Emilia78 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Emilia78 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Emilia78 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
put on hold as off-topic by user10354138, saz, Davide Giraudo, Cesareo, Alexander Gruber♦ 2 days ago
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – user10354138, saz, Davide Giraudo, Cesareo, Alexander Gruber
If this question can be reworded to fit the rules in the help center, please edit the question.
put on hold as off-topic by user10354138, saz, Davide Giraudo, Cesareo, Alexander Gruber♦ 2 days ago
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – user10354138, saz, Davide Giraudo, Cesareo, Alexander Gruber
If this question can be reworded to fit the rules in the help center, please edit the question.
2
Welcome to MSE. It will be more likely that you will get an answer if you show us that you made an effort. This should be added to the question rather than in the comments.
– José Carlos Santos
Nov 13 at 10:08
Consider formatting your question clearly by putting the math parts enclosed in $ .
– Gautam Shenoy
Nov 13 at 10:09
It would be easy if it was true that whenever $E[1_BY_n] rightarrow 0 $ for every set $B in mathcal{G}$, than $Y_n rightarrow 0$ a.s. . , but I do not know if this is true... Is somebody can point a reference of such a result I can write the simple reasonings...
– Thomas
Nov 13 at 17:46
add a comment |
2
Welcome to MSE. It will be more likely that you will get an answer if you show us that you made an effort. This should be added to the question rather than in the comments.
– José Carlos Santos
Nov 13 at 10:08
Consider formatting your question clearly by putting the math parts enclosed in $ .
– Gautam Shenoy
Nov 13 at 10:09
It would be easy if it was true that whenever $E[1_BY_n] rightarrow 0 $ for every set $B in mathcal{G}$, than $Y_n rightarrow 0$ a.s. . , but I do not know if this is true... Is somebody can point a reference of such a result I can write the simple reasonings...
– Thomas
Nov 13 at 17:46
2
2
Welcome to MSE. It will be more likely that you will get an answer if you show us that you made an effort. This should be added to the question rather than in the comments.
– José Carlos Santos
Nov 13 at 10:08
Welcome to MSE. It will be more likely that you will get an answer if you show us that you made an effort. This should be added to the question rather than in the comments.
– José Carlos Santos
Nov 13 at 10:08
Consider formatting your question clearly by putting the math parts enclosed in $ .
– Gautam Shenoy
Nov 13 at 10:09
Consider formatting your question clearly by putting the math parts enclosed in $ .
– Gautam Shenoy
Nov 13 at 10:09
It would be easy if it was true that whenever $E[1_BY_n] rightarrow 0 $ for every set $B in mathcal{G}$, than $Y_n rightarrow 0$ a.s. . , but I do not know if this is true... Is somebody can point a reference of such a result I can write the simple reasonings...
– Thomas
Nov 13 at 17:46
It would be easy if it was true that whenever $E[1_BY_n] rightarrow 0 $ for every set $B in mathcal{G}$, than $Y_n rightarrow 0$ a.s. . , but I do not know if this is true... Is somebody can point a reference of such a result I can write the simple reasonings...
– Thomas
Nov 13 at 17:46
add a comment |
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Welcome to MSE. It will be more likely that you will get an answer if you show us that you made an effort. This should be added to the question rather than in the comments.
– José Carlos Santos
Nov 13 at 10:08
Consider formatting your question clearly by putting the math parts enclosed in $ .
– Gautam Shenoy
Nov 13 at 10:09
It would be easy if it was true that whenever $E[1_BY_n] rightarrow 0 $ for every set $B in mathcal{G}$, than $Y_n rightarrow 0$ a.s. . , but I do not know if this is true... Is somebody can point a reference of such a result I can write the simple reasonings...
– Thomas
Nov 13 at 17:46