Aims and Scope

The Open Mathematics, Statistics and Probability Journal is an Open Access online journal, which publishes research articles, full-length and mini-reviews, letters and guest edited single topic issues in all important areas of statistics and probability. All areas of statistics are covered including biostatistics, stochastic geometry and algorithms, statistical mechanics, ergodic theory, mathematical biology and bioinformatics, applied commutative algebra, experimental mathematics, convexity theory, discrete mathematics, filtering theory, theoretical computer science and optimization.

The Open Mathematics, Statistics and Probability Journal , a peer-reviewed journal, is an important and reliable source of current information on developments in the field. The emphasis will be on publishing quality papers rapidly and making them freely available to researchers worldwide.

Editor's Choice

Comparing Different Information Levels

Uwe Saint-Mont


Given a sequence of random variables X = X1, X2, . . .suppose the aim is to maximize one’s return by picking a ‘favorable’ Xi. Obviously, the expected payoff crucially depends on the information at hand. An optimally informed person knows all the values Xi = xi and thus receives E(sup Xi).


We will compare this return to the expected payoffs of a number of gamblers having less information, in particular supi(EXi), the value of the sequence to a person who only knows the random variables’ expected values.

In general, there is a stochastic environment, (F.E. a class of random variables C), and several levels of information. Given some XϵC, an observer possessing information j obtains rj(X). We are going to study ‘information sets’ of the form.

characterizing the advantage of k relative to j. Since such a set measures the additional payoff by virtue of increased information, its analysis yields a number of interesting results, in particular ‘prophet-type’ inequalities.

July 19, 2017

Quick Links

Indexing Agencies