Related papers: Kolmogorov and Aleksandrov in Sevan Monastery, Arm…
Summer vacations in the Dolomites were a tradition among the professors of the Faculty of Mathematical and Physical Sciences at the University of Roma since the end of the XIX century. Beyond the academic walls, people like Tullio…
There is a good cause to assert that the Easter Islanders constantly watched Aldebaran and the Pleiades in the past. The Russian scholar Irina K. Fedorova and the American scholar Georgia Lee were the first who contributed significantly to…
Some established and also novel techniques in the field of applications of algorithmic (Kolmogorov) complexity currently co-exist for the first time and are here reviewed, ranging from dominant ones such as statistical lossless compression…
A selection of the relevant theorems of Probability Theory that comes directly from Kolmogorov's axioms, Set Theory basic results, definitions and rules of inference are listed and proven in a systematic approach, aiming the student who…
Twenty years ago, in October 1990, I found myself attending a workshop on Theoretical Physics in Chernomorka (Ukraine) intended only for Soviet physicists. That trip to the USSR/CCCP as well as the preceding months at CERN were highly…
The Daniell-Kolmogorov Extension Theorem is a fundamental result in the theory of stochastic processes, as it allows one to construct a stochastic process with prescribed finite-dimensional distributions. However, it is well-known that the…
In this brief note, there is a short recollection of my scientific interactions with the great Russian mathematician Sergey Konstantinovich Godunov.
Kolmogorov's first axiom of probability is probability takes values between 0 and 1; however, in Cox's derivation of probability having a maximum value of unity is arbitrary since he derives probability as a tool to rank degrees of…
We develop an analogue of probability theory for probabilities taking values in topological groups. We generalize Kolmogorov's method of axiomatization of probability theory: main distinguishing features of frequency probabilities are taken…
PhD Thesis under the supervision of Professor Nedyalko Nenov.
(Write-up of a talk at the Bialowieza meeting, July 2007.) Gelfand and Kolmogorov in 1939 proved that a compact Hausdorff topological space $X$ can be canonically embedded into the infinite-dimensional vector space $C(X)^* $, the dual space…
This article, the second in a series about the Russian scientist Mikhail Lomonosov (1711-1765), traces his education from his arrival in Moscow in 1731 to study at the Slavo-Greco-Latin Academy, through his admission to the St. Petersburg…
Using the ideas of abstract algebra, we introduce the basic concepts of abstract probability theory that generalize the Kolmogorov's probability theory, possibility theory and other theories that deal with uncertainty. Based on abstract…
Using the approach of N. Etemadi for the Strong Law of Large Numbers (SLLN) from 1981 and the elaboration of this approach by S. Cs\"org\H{o}, K. Tandori and V. Totik from 1983, I give weak conditions under which the SLLN still holds for…
This article, the third in a series about the Russian scientist Mikhail Lomonosov (1711-1765), covers the first decade of his research at the St. Petersburg Academy of Sciences, from his return from an educational his trip abroad in 1741,…
This paper begins with a study of the exact distribution of the empirical correlation of two independent AR(1) processes with Gaussian increments. We proceed to develop rates of convergence for the distribution of the scaled empirical…
The entropy of a finite probability space $X$ measures the observable cardinality of large independent products $X^{\otimes n}$ of the probability space. If two probability spaces $X$ and $Y$ have the same entropy, there is an almost…
Key figure of Russian Enlightenment, polymath Mikhail Vasilievich Lomonosov (1711-1765) had discovered atmosphere of Venus during its transit over the Sun's disc in 1761. This paper contains the first full English translation of his report…
The paper deals with the order statistics and empirical mathematical expectation (which is also called the estimate of mathematical expectation in the literature) in the case of infinitely increasing random variables. The Kolmogorov concept…
We consider the symmetric rendezvous search game on a complete graph of n locations. In 1990, Anderson and Weber proposed a strategy in which, over successive blocks of n-1 steps, the players independently choose either to stay at their…