Weakly dependent chains with infinite memory

Details Weakly dependent chains with infinite memory Weakly dependent chains with infinite memory

2007-12-19

arxiv.org/abs/0712.3231v1

Mathematics

Probability

Stochastic Processes and their Applications (2008) accept\'e

Scientific paper

We prove the existence of a weakly dependent strictly stationary solution of the equation $ X_t=F(X_{t-1},X_{t-2},X_{t-3},...;\xi_t)$ called {\em chain with infinite memory}. Here the {\em innovations} $\xi_t$ constitute an independent and identically distributed sequence of random variables. The function $F$ takes values in some Banach space and satisfies a Lipschitz-type condition. We also study the interplay between the existence of moments and the rate of decay of the Lipschitz coefficients of the function $F$. With the help of the weak dependence properties, we derive Strong Laws of Large Number, a Central Limit Theorem and a Strong Invariance Principle.

Affiliated with

Also associated with

No associations

Rating

Weakly dependent chains with infinite memory does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Weakly dependent chains with infinite memory, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Weakly dependent chains with infinite memory will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-147167