Occupation times

CDSNS Colloquium
Monday, April 2, 2018 - 11:15
1 hour (actually 50 minutes)
skiles 005
Penn State University
Consider a $T$-preserving probability measure $m$ on a  dynamical system $T:X\to X$. The occupation time of a measurable function is the sequence $\ell_n(A,x)$   ($A\subset \mathbb R, x\in X$) defined as the number of $j\le n$ for which the partial sums $S_jf(x)\in A$.  The talk will discuss conditions which ensure that this sequence, properly normed, converges weakly to some limit distribution. It turns out that this distribution is Mittag-Leffler and in particular the result covers the case when $f\circ T^j$ is a fractal Gaussian noise of Hurst parameter $>3/4$.