b*******e
发帖数: 55 | 1 Let (Ω, B, P) be ([0,1], B[0,1], λ) where λ is Lebesgue measure on [0,
1]. Define the
process {Xt, 0<=t<=1} by
Xt(w)=0 if t not equal w
1 if t= w
So I can prove that Xt is a random variable.
For the sigma-field generated by {Xt, 0<=t<=1}
Sigma ({Xt, 0<=t<=1})=Sigma (Ut sigma(Xt)), where sigma (Xt) ={Ω, ∅,
{t}, [0,1]\{t}}
is this right?
I guess I am not so clear here for a sigma field generated by {Xt, 0<=t<=1}
Thanks a million！ | Q***5
发帖数: 994 | 2 The sigma field generated by {Xt, 0<=t<=1} consists of the sets either
countable or whose complement ([0 1] \ the set) is countable.
0,
,
【在 b*******e 的大作中提到】
: Let (Ω, B, P) be ([0,1], B[0,1], λ) where λ is Lebesgue measure on [0,
: 1]. Define the
: process {Xt, 0<=t<=1} by
: Xt(w)=0 if t not equal w
: 1 if t= w
: So I can prove that Xt is a random variable.
: For the sigma-field generated by {Xt, 0<=t<=1}
: Sigma ({Xt, 0<=t<=1})=Sigma (Ut sigma(Xt)), where sigma (Xt) ={Ω, ∅,
: {t}, [0,1]\{t}}
: is this right?
| b*******e
发帖数: 55 | 3 Thanks, QL365.
I knew the result. I need to prove it.
I finished most of the prove, just want to make sure some steps that I used
during the proof is right. |
|
