Mode of the stationary distribution
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From a course on SDE's. We consider a general, stationary advection-diffusion equation.
$left(uC-DC'right)'=0$
We wish to show that stationary points are those at which $u=0$ and use this to find the mode of a stationary distribution in a Cox-Ingersoll_Ross process.
Integrating once, we get the form, if we assume $C(0)=0$.
$C'=-uC/D$
But only if we assume that IC, will it make it a stationary point. Is this the way to do it?
Furthermore, what does it have to do with the mode? I could not find a different definition from the statistical one of most frequent observation.
probability-theory stochastic-processes stochastic-calculus sde
asked Nov 28 at 1:05
thaumoctopus
11117
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up vote
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From a course on SDE's. We consider a general, stationary advection-diffusion equation.
$left(uC-DC'right)'=0$
We wish to show that stationary points are those at which $u=0$ and use this to find the mode of a stationary distribution in a Cox-Ingersoll_Ross process.
Integrating once, we get the form, if we assume $C(0)=0$.
$C'=-uC/D$
But only if we assume that IC, will it make it a stationary point. Is this the way to do it?
Furthermore, what does it have to do with the mode? I could not find a different definition from the statistical one of most frequent observation.
probability-theory stochastic-processes stochastic-calculus sde
asked Nov 28 at 1:05
thaumoctopus
11117
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
From a course on SDE's. We consider a general, stationary advection-diffusion equation.
$left(uC-DC'right)'=0$
We wish to show that stationary points are those at which $u=0$ and use this to find the mode of a stationary distribution in a Cox-Ingersoll_Ross process.
Integrating once, we get the form, if we assume $C(0)=0$.
$C'=-uC/D$
But only if we assume that IC, will it make it a stationary point. Is this the way to do it?
Furthermore, what does it have to do with the mode? I could not find a different definition from the statistical one of most frequent observation.
probability-theory stochastic-processes stochastic-calculus sde
asked Nov 28 at 1:05
thaumoctopus
11117
From a course on SDE's. We consider a general, stationary advection-diffusion equation.
$left(uC-DC'right)'=0$
We wish to show that stationary points are those at which $u=0$ and use this to find the mode of a stationary distribution in a Cox-Ingersoll_Ross process.
Integrating once, we get the form, if we assume $C(0)=0$.
$C'=-uC/D$
But only if we assume that IC, will it make it a stationary point. Is this the way to do it?
Furthermore, what does it have to do with the mode? I could not find a different definition from the statistical one of most frequent observation.
probability-theory stochastic-processes stochastic-calculus sde
probability-theory stochastic-processes stochastic-calculus sde
asked Nov 28 at 1:05
thaumoctopus
11117
asked Nov 28 at 1:05
thaumoctopus
11117
edited Nov 28 at 23:17
asked Nov 28 at 1:05
thaumoctopus
11117
asked Nov 28 at 1:05
thaumoctopus
11117
asked Nov 28 at 1:05
thaumoctopus
11117
11117
add a comment |
add a comment |
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