Operator averages

Specially Weighted Moving Averages with Repeated Application of the Ema Operator

Moving Averages

More generally, weighted averages may also be used. Moving averages are also called running means or rolling averages. They are a special case of “filtering”, which is a general process that takes one time series and transforms it into another time series. The term “moving average” is used to describe this procedure because each average is computed by dropping the oldest observation and includi...

Kahane-Khinchin type Averages

We prove a Kahane-Khinchin type result with a few random vectors, which are distributed independently with respect to an arbitrary log-concave probability measure on Rn. This is an application of small ball estimate and Chernoff’s method, that has been recently used in the context of Asymptotic Geometric Analysis in [1], [2].

Characteristic Functions and Averages

Let Ω be a set and Ω1, . . . ,Ωm−1 subsets of Ω, being m an integer greater than one. For a given function f = (f1, . . . fm) : Ω → R, we prove the existence of a unique function α = (α1, . . . , αm) : Ω → R m such that

Thermodynamics and Time–averages

For a dynamical system far from equilibrium, one has to deal with empirical probabilities defined through time–averages, and the main problem is then how to formulate an appropriate statistical thermodynamics. The common answer is that the standard functional expression of Boltzmann-Gibbs for the entropy should be used, the empirical probabilities being substituted for the Gibbs measure. Other ...