- #1
Tetef
- 3
- 0
Hi,
Letting [itex]W[/itex] be a standard brownian motion, we define the first hitting times
[itex]T_{a}=inf\{t:W(t)=a\}[/itex] with [itex]a<0[/itex]
and
[itex]T_{b}=inf\{t:W(t)=b\}[/itex] with [itex]b>0[/itex]
The probability of one hitting time being before an other is :
[itex]P\{T_{a}<T_{b}\}=\frac{b}{b-a}[/itex]
I'm looking for this probability in the case of a brownian bridge :
[itex]P\{T_{a}<T_{b} | W(t)=x\}[/itex] with [itex]x<a[/itex]
Could some one help me please?
Thx !
Letting [itex]W[/itex] be a standard brownian motion, we define the first hitting times
[itex]T_{a}=inf\{t:W(t)=a\}[/itex] with [itex]a<0[/itex]
and
[itex]T_{b}=inf\{t:W(t)=b\}[/itex] with [itex]b>0[/itex]
The probability of one hitting time being before an other is :
[itex]P\{T_{a}<T_{b}\}=\frac{b}{b-a}[/itex]
I'm looking for this probability in the case of a brownian bridge :
[itex]P\{T_{a}<T_{b} | W(t)=x\}[/itex] with [itex]x<a[/itex]
Could some one help me please?
Thx !