An ergodic theorem of arithmetic type

In: Tatra Mountains Mathematical Publications, vol. 31, no. 2

Michel Weber

Detaily:

Rok, strany: 2005, 123 - 129

O článku:

Let $d(n)$ be the divisor function. Let $X₁,X₂,…$ be a sequence of centered iid random variables. We obtain strong laws of large numbers for the sums $∑_n=1^N d(n) X_n$. Let $τ$ be any ergodic endomorphism of the torus $T$. We also establish a universal ergodic theorem, which in particular implies for any square integrable function $f$, that

$$ łim_N o∞{∑_n=1^N pm d(n) fcircτⁿ(x) over ∑_n=1^N d(n)}=0 , $$

for almost all $x$, where the random signs are independent.

Ako citovať:

ISO 690:

Weber, M. 2005. An ergodic theorem of arithmetic type. In Tatra Mountains Mathematical Publications, vol. 31, no.2, pp. 123-129. 1210-3195.

APA:

Weber, M. (2005). An ergodic theorem of arithmetic type. Tatra Mountains Mathematical Publications, 31(2), 123-129. 1210-3195.