[转载] Also a simulation problem.# Computation - 科学计算
w*d
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【 以下文字转载自 Mathematics 讨论区 】
【 原文由 wind 所发表 】
1) original problem:
a random field( process) w(x), x \in (0, pi).
The mean is zero everywhere.
Covariance function c(x1,x2) = exp(-|x1-x2|/b ), b>0
We also know the PDF of w(x) for any fixed x.
How to do the simulation?
2) simplified(approximated) version:
Use Karhunen-Loeve expansion of w(x), to obtain an approximation:
w(x) = f(x) alpha1 + g(x) alpha2
then both alpha1 and alpha2 have the given PDF, and are uncorrelated.
After this, the prob
【 原文由 wind 所发表 】
1) original problem:
a random field( process) w(x), x \in (0, pi).
The mean is zero everywhere.
Covariance function c(x1,x2) = exp(-|x1-x2|/b ), b>0
We also know the PDF of w(x) for any fixed x.
How to do the simulation?
2) simplified(approximated) version:
Use Karhunen-Loeve expansion of w(x), to obtain an approximation:
w(x) = f(x) alpha1 + g(x) alpha2
then both alpha1 and alpha2 have the given PDF, and are uncorrelated.
After this, the prob