In this paper we revisit the Bialynicki-Birula and Mycielski uncertainty principle and its cases of equality. This Shannon entropic version of the well-known Heisenberg uncertainty principle can be used when dealing with variables that admit no variance. In this paper, we extend this uncertainty...

In this paper, a natural extension of the Lempel–Ziv complexity for several finite-time sequences, defined on finite size alphabets is proposed. Some results on the defined joint Lempel–Ziv complexity are given, as well as properties in connection with the Lempel–Ziv complexity of the...

Ebrahimi and Pellerey (1995) and Ebrahimi (1996) proposed the Shannon residual entropy function as a useful dynamic measure of uncertainty. They studied the characterization problem from the residual entropy. They also used this function to define a stochastic order and two classes of...

Scientific analysis of the linguistic styles of different authors has generated considerable interest. We present a generic approach to measuring the similarity of two symbolic sequences that requires minimal background knowledge about a given human language. Our analysis is based on word rank...

A quantitative check of efficiency in US dollar/Deutsche mark exchange rates is developed using high-frequency (tick by tick) data. The antipersistent Markov behavior of log-price fluctuations of given size implies, in principle, the possibility of a statistical forecast. We introduce and...