What does $sum_{k=1}^{infty}X_k a_{n,k}$ exists almost surely for each $n$, actually mean?
Prove that $sum_{k=1}^{infty}X_k a_{n,k}$ exists almost surely for each $n$.
Is it that $Pbigg(displaystylelim_{nrightarrowinfty}sum_{k=1}^{infty}X_ka_{n,k}<inftybigg)=1$?
In this case $X_k$ is a sequence of random variables and $a_{n,k}$ are elements of a regular matrix.
I'm just confused on the wording, thanks!
probability sequences-and-series measure-theory terminology definition
asked Nov 25 at 4:23
OGV
497
|
show 3 more comments
Prove that $sum_{k=1}^{infty}X_k a_{n,k}$ exists almost surely for each $n$.
Is it that $Pbigg(displaystylelim_{nrightarrowinfty}sum_{k=1}^{infty}X_ka_{n,k}<inftybigg)=1$?
In this case $X_k$ is a sequence of random variables and $a_{n,k}$ are elements of a regular matrix.
I'm just confused on the wording, thanks!
probability sequences-and-series measure-theory terminology definition
asked Nov 25 at 4:23
OGV
497
Yes. [More character for comment to appear.]
– Will M.
Nov 25 at 4:28
@WillM.: In future, try${}{}{}{}{}$. It disappears.
– Shaun
Nov 25 at 4:29
2
I cannot make sense of the question. There is no $n$ in the statement, only $n_k$ -- how do these symbols relate?
– Clement C.
Nov 25 at 4:41
Actually double apologies, just to be clear, my question is written as $a_{nk}$ but what this must be referring to is $a_{n,k}$ so we're all clear then
– OGV
Nov 25 at 5:18
Proving that, for every fixed $n$, $mathbb{E}[sum_{k=1}^infty X_k a_{n,k}]$ exists would imply the result.
– Clement C.
Nov 25 at 5:28
|
show 3 more comments
Prove that $sum_{k=1}^{infty}X_k a_{n,k}$ exists almost surely for each $n$.
Is it that $Pbigg(displaystylelim_{nrightarrowinfty}sum_{k=1}^{infty}X_ka_{n,k}<inftybigg)=1$?
In this case $X_k$ is a sequence of random variables and $a_{n,k}$ are elements of a regular matrix.
I'm just confused on the wording, thanks!
probability sequences-and-series measure-theory terminology definition
asked Nov 25 at 4:23
OGV
497
Prove that $sum_{k=1}^{infty}X_k a_{n,k}$ exists almost surely for each $n$.
Is it that $Pbigg(displaystylelim_{nrightarrowinfty}sum_{k=1}^{infty}X_ka_{n,k}<inftybigg)=1$?
In this case $X_k$ is a sequence of random variables and $a_{n,k}$ are elements of a regular matrix.
I'm just confused on the wording, thanks!
probability sequences-and-series measure-theory terminology definition
probability sequences-and-series measure-theory terminology definition
asked Nov 25 at 4:23
OGV
497
asked Nov 25 at 4:23
OGV
497
edited Nov 25 at 5:17
asked Nov 25 at 4:23
OGV
497
asked Nov 25 at 4:23
OGV
497
asked Nov 25 at 4:23
OGV
497
497
Yes. [More character for comment to appear.]
– Will M.
Nov 25 at 4:28
@WillM.: In future, try${}{}{}{}{}$. It disappears.
– Shaun
Nov 25 at 4:29
2
I cannot make sense of the question. There is no $n$ in the statement, only $n_k$ -- how do these symbols relate?
– Clement C.
Nov 25 at 4:41
Actually double apologies, just to be clear, my question is written as $a_{nk}$ but what this must be referring to is $a_{n,k}$ so we're all clear then
– OGV
Nov 25 at 5:18
Proving that, for every fixed $n$, $mathbb{E}[sum_{k=1}^infty X_k a_{n,k}]$ exists would imply the result.
– Clement C.
Nov 25 at 5:28
|
show 3 more comments
Yes. [More character for comment to appear.]
– Will M.
Nov 25 at 4:28
@WillM.: In future, try${}{}{}{}{}$. It disappears.
– Shaun
Nov 25 at 4:29
2
I cannot make sense of the question. There is no $n$ in the statement, only $n_k$ -- how do these symbols relate?
– Clement C.
Nov 25 at 4:41
Actually double apologies, just to be clear, my question is written as $a_{nk}$ but what this must be referring to is $a_{n,k}$ so we're all clear then
– OGV
Nov 25 at 5:18
Proving that, for every fixed $n$, $mathbb{E}[sum_{k=1}^infty X_k a_{n,k}]$ exists would imply the result.
– Clement C.
Nov 25 at 5:28
Yes. [More character for comment to appear.]
– Will M.
Nov 25 at 4:28
Yes. [More character for comment to appear.]
– Will M.
Nov 25 at 4:28
@WillM.: In future, try
${}{}{}{}{}$. It disappears.– Shaun
Nov 25 at 4:29
@WillM.: In future, try
${}{}{}{}{}$. It disappears.– Shaun
Nov 25 at 4:29
2
2
I cannot make sense of the question. There is no $n$ in the statement, only $n_k$ -- how do these symbols relate?
– Clement C.
Nov 25 at 4:41
I cannot make sense of the question. There is no $n$ in the statement, only $n_k$ -- how do these symbols relate?
– Clement C.
Nov 25 at 4:41
Actually double apologies, just to be clear, my question is written as $a_{nk}$ but what this must be referring to is $a_{n,k}$ so we're all clear then
– OGV
Nov 25 at 5:18
Actually double apologies, just to be clear, my question is written as $a_{nk}$ but what this must be referring to is $a_{n,k}$ so we're all clear then
– OGV
Nov 25 at 5:18
Proving that, for every fixed $n$, $mathbb{E}[sum_{k=1}^infty X_k a_{n,k}]$ exists would imply the result.
– Clement C.
Nov 25 at 5:28
Proving that, for every fixed $n$, $mathbb{E}[sum_{k=1}^infty X_k a_{n,k}]$ exists would imply the result.
– Clement C.
Nov 25 at 5:28
|
show 3 more comments
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Yes. [More character for comment to appear.]
– Will M.
Nov 25 at 4:28
@WillM.: In future, try
${}{}{}{}{}$. It disappears.– Shaun
Nov 25 at 4:29
2
I cannot make sense of the question. There is no $n$ in the statement, only $n_k$ -- how do these symbols relate?
– Clement C.
Nov 25 at 4:41
Actually double apologies, just to be clear, my question is written as $a_{nk}$ but what this must be referring to is $a_{n,k}$ so we're all clear then
– OGV
Nov 25 at 5:18
Proving that, for every fixed $n$, $mathbb{E}[sum_{k=1}^infty X_k a_{n,k}]$ exists would imply the result.
– Clement C.
Nov 25 at 5:28