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simulation of a set of stochastic ODE

simulation of a set of stochastic ODE# Computation - 科学计算

r*y2005-03-28 08:03

1 楼

For a set of stochastic ODE
dX/dt = A*X + F*e,
where e is white noise with known variance and mean
I know how to do without noise term. But with the noise term, what is the
most common way to do the simulation? Generate a bunch of random numbers first
then add them in one by one? Or a more "educated" method than this?

h*o2005-03-28 08:03

2 楼

need more detail about F and e
if F and e have good features, X is a Guassian distribution, its mean and
variance can be obtained by solving two ODEs.
Otherwise, Monte Carlo

【在 r****y 的大作中提到】

: For a set of stochastic ODE
: dX/dt = A*X + F*e,
: where e is white noise with known variance and mean
: I know how to do without noise term. But with the noise term, what is the
: most common way to do the simulation? Generate a bunch of random numbers first
: then add them in one by one? Or a more "educated" method than this?
:

r*y2005-03-28 08:03

3 楼

actually X is a set of variables. Here I am sovling a stochastic ODEs, not
just one.
Let me flip coin for the question: I have raw time series for a bunch of
variables. Someone said they all can be well simulated using stochastic ODEs.
So he goes ahead and use dX/dt = A*X + F*e to fit my time series. Now if I
wanna test how good such stochastic ODEs can predict future time series, which
way is the most effective way to tell?
Thanks. :-)
the
first

【在 h***o 的大作中提到】

: need more detail about F and e
: if F and e have good features, X is a Guassian distribution, its mean and
: variance can be obtained by solving two ODEs.
: Otherwise, Monte Carlo

h*o2005-03-28 08:03

4 楼

read read some stat book ba...there should be some standard ways to test
this kind of conclusions.

【在 r****y 的大作中提到】

:
: actually X is a set of variables. Here I am sovling a stochastic ODEs, not
: just one.
: Let me flip coin for the question: I have raw time series for a bunch of
: variables. Someone said they all can be well simulated using stochastic ODEs.
: So he goes ahead and use dX/dt = A*X + F*e to fit my time series. Now if I
: wanna test how good such stochastic ODEs can predict future time series, which
: way is the most effective way to tell?
: Thanks. :-)
: the

r*y2005-03-28 08:03

5 楼

Any good recommendations? I browsed several stat books, but none
直重要害。

【在 h***o 的大作中提到】

: read read some stat book ba...there should be some standard ways to test
: this kind of conclusions.

h*o2005-03-28 08:03

6 楼

try try some time series books....u'd better ask in stat board

【在 r****y 的大作中提到】

:
: Any good recommendations? I browsed several stat books, but none
: 直重要害。

f*r2005-03-28 08:03

7 楼

I have the same problem. Just borrowed a stochastic differential equatio
ns book and I am still learning. Cannot answer your question now. //Hany
an

【在 r****y 的大作中提到】

:
: Any good recommendations? I browsed several stat books, but none
: 直重要害。

f*r2005-03-28 08:03

8 楼

Here is one article maybe helpful
http://epubs.siam.org/sam-bin/dbq/article/37830

【在 r****y 的大作中提到】

:
: Any good recommendations? I browsed several stat books, but none
: 直重要害。