On the invariant measure of the random difference equation $X_n=A_n X_{n-1}+ B_n$ in the critical case

Details On the invariant measure of the random difference equation $X_n=A_n X_{n-1}+ B_n$ in the critical case On the invariant measure of the random difference equation $X_n=A_n X_{n-1}+ B_n$ in the critical case

2008-09-10

arxiv.org/abs/0809.1864v2

Mathematics

Probability

Scientific paper

We consider the autoregressive model on $\R^d$ defined by the following stochastic recursion $X_n = A_n X_{n-1}+B_n$, where $\{(B_n,A_n)\}$ are i.i.d. random variables valued in $\R^d\times \R^+$. The critical case, when $\E\big[\log A_1\big]=0$, was studied by Babillot, Bougeorol and Elie, who proved that there exists a unique invariant Radon measure $\nu$ for the Markov chain $\{X_n \}$. In the present paper we prove that the weak limit of properly dilated measure $\nu$ exists and defines a homogeneous measure on $\R^d\setminus \{0\}$.

Affiliated with

Also associated with

No associations

Rating

On the invariant measure of the random difference equation $X_n=A_n X_{n-1}+ B_n$ in the critical case 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 On the invariant measure of the random difference equation $X_n=A_n X_{n-1}+ B_n$ in the critical case, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the invariant measure of the random difference equation $X_n=A_n X_{n-1}+ B_n$ in the critical case will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-161995