Stable age distribution The Next CEO of Stack OverflowIs this action of $mathbb F[[x]]$ on $bigoplus_i=0^inftymathbb F$ natural?Backward stable algorithmis the system exponentially stable? uniformly stable?Determining the derivation of a determinantMatrix of $phi$-stable operatorsGenerate a random neutrally stable matrixLeslie matrix and stable age distribution.Stable Matrices?Stable way to find QR-decompositionconvex combination of two stable matrices
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Stable age distribution
The Next CEO of Stack OverflowIs this action of $mathbb F[[x]]$ on $bigoplus_i=0^inftymathbb F$ natural?Backward stable algorithmis the system exponentially stable? uniformly stable?Determining the derivation of a determinantMatrix of $phi$-stable operatorsGenerate a random neutrally stable matrixLeslie matrix and stable age distribution.Stable Matrices?Stable way to find QR-decompositionconvex combination of two stable matrices
$begingroup$
Let $n_tin R^m_++$ be an $m$-dimensional population distribution with ages $0,1,ldots,m-1$. Then, this distribution is stable if
$$
n_t+1=A n_t
$$
for some $mtimes m$ transition matrix $A$. Suppose people at every age $i$ die with probability $e_i$ and people of oldest age die with probability $1$. That is,
$$
A = left(beginarrayccccc
e_0 & e_1 &ldots & e_m-2 & 1 \
1-e_0 & 0& ldots & 0 & 0 \
0 & 1-e_1& ldots & 0 & 0 \
vdots & ddots & ddots & 0 & 0 \
0 & 0& ldots & 1-e_m-2 & 0
endarray right)
$$
As $det (A-I)=0$ the age distribution is stable.
Question: how can I generalize this argument to infinite $m$? Are there any extra conditions I need to impose?
matrices determinant
asked yesterday
AlexAlex
233
$endgroup$
add a comment |
$begingroup$
Let $n_tin R^m_++$ be an $m$-dimensional population distribution with ages $0,1,ldots,m-1$. Then, this distribution is stable if
$$
n_t+1=A n_t
$$
for some $mtimes m$ transition matrix $A$. Suppose people at every age $i$ die with probability $e_i$ and people of oldest age die with probability $1$. That is,
$$
A = left(beginarrayccccc
e_0 & e_1 &ldots & e_m-2 & 1 \
1-e_0 & 0& ldots & 0 & 0 \
0 & 1-e_1& ldots & 0 & 0 \
vdots & ddots & ddots & 0 & 0 \
0 & 0& ldots & 1-e_m-2 & 0
endarray right)
$$
As $det (A-I)=0$ the age distribution is stable.
Question: how can I generalize this argument to infinite $m$? Are there any extra conditions I need to impose?
matrices determinant
asked yesterday
AlexAlex
233
$endgroup$
add a comment |
$begingroup$
Let $n_tin R^m_++$ be an $m$-dimensional population distribution with ages $0,1,ldots,m-1$. Then, this distribution is stable if
$$
n_t+1=A n_t
$$
for some $mtimes m$ transition matrix $A$. Suppose people at every age $i$ die with probability $e_i$ and people of oldest age die with probability $1$. That is,
$$
A = left(beginarrayccccc
e_0 & e_1 &ldots & e_m-2 & 1 \
1-e_0 & 0& ldots & 0 & 0 \
0 & 1-e_1& ldots & 0 & 0 \
vdots & ddots & ddots & 0 & 0 \
0 & 0& ldots & 1-e_m-2 & 0
endarray right)
$$
As $det (A-I)=0$ the age distribution is stable.
Question: how can I generalize this argument to infinite $m$? Are there any extra conditions I need to impose?
matrices determinant
asked yesterday
AlexAlex
233
$endgroup$
Let $n_tin R^m_++$ be an $m$-dimensional population distribution with ages $0,1,ldots,m-1$. Then, this distribution is stable if
$$
n_t+1=A n_t
$$
for some $mtimes m$ transition matrix $A$. Suppose people at every age $i$ die with probability $e_i$ and people of oldest age die with probability $1$. That is,
$$
A = left(beginarrayccccc
e_0 & e_1 &ldots & e_m-2 & 1 \
1-e_0 & 0& ldots & 0 & 0 \
0 & 1-e_1& ldots & 0 & 0 \
vdots & ddots & ddots & 0 & 0 \
0 & 0& ldots & 1-e_m-2 & 0
endarray right)
$$
As $det (A-I)=0$ the age distribution is stable.
Question: how can I generalize this argument to infinite $m$? Are there any extra conditions I need to impose?
matrices determinant
matrices determinant
asked yesterday
AlexAlex
233
asked yesterday
AlexAlex
233
asked yesterday
AlexAlex
233
asked yesterday
AlexAlex
233
asked yesterday
AlexAlex
233
233
add a comment |
add a comment |
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active
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