- #1
rickywaldron
- 8
- 0
I'm having a bit of a problem proving the second condition for a martingale, the discrete time branching process Z(n)=X(n)/m^n, where m is the mean number of offspring per individual and X(n) is the size of the nth generation.
I have E[z(n)]=E[x(n)]/m^n=m^n/m^n (from definition E[X^n]=m^n) = 1
which is less than infinity, so first condition passes
Then I get lost with E[Z(n+1) given X(1),X(2)...X(n)]...any clues on how to show this is equal to Z(n)? Thanks
I have E[z(n)]=E[x(n)]/m^n=m^n/m^n (from definition E[X^n]=m^n) = 1
which is less than infinity, so first condition passes
Then I get lost with E[Z(n+1) given X(1),X(2)...X(n)]...any clues on how to show this is equal to Z(n)? Thanks