asymptotoic behaviour of inverse of a stochastic matrix

oercim · science forum beginner Joined: 04 May 2005 Posts: 40

Hello. Can someone help me please?
Let D be m*m stochastic matrix and let expected value of D is
E(D). Let,

D=sum(j=1 to j)(dj*dj) where dj are m*1 vectors. And let

E(D)=O(n) , D=Op(n), D-E(D)=Op(sqrt(n)),

where O denotes deterministic order of magnitude and Op
denotes stochastic order of magnitude. Then we have,

D^(-1) = (E(D)^(-1)) - (E(D))^(-1)*(D - E(D))*(E(D))^(-1) +
Op(n(-2)).

How can this be? Why? If someone explain this to me , I will
be very approcaite. Thanks alot.

Google