Anticipating a Hundred Years of Modern Probability and Stochastic Processes

Dear Colleagues,

Axiomatic probability and mathematical stochastic processes are relatively young subjects. Indeed, it has been a mere ninety years since the so-called heroic period of mathematical probability theory, where, among other important works, Kolmogorov wrote the Axioms of Probability and Khinchin gave the first mathematical description of a Stochastic Process. Yet, they have experienced spectacular growth and appear to be in the middle of many interesting developments that may shape the next ten years of research. It is interesting to recount what some probability and stochastic processes have become and, at the risk of embarrassment, anticipate their potential role in the next ten years. This inaugural Special Issue is dedicated to launching the celebration of the first one hundred years of modern probability and stochastic processes. It will include a special historical tribute paper to some of the heroic contributions of the 1930s which commenced new ways of thinking. Any novel theoretical or applied research contribution related to probability or stochastic processes will be considered. All contributors are encouraged to include paragraphs about the history and the anticipated future of their subject of writing. Connections to modern applications are encouraged.

Probability theory provides the mathematical framework to describe, model, analyze, and solve problems with random phenomena. Stochastic processes are probabilistic models for random quantities evolving in time or space. They have significant applications in many areas, including gambling, economics, operations research, discrete mathematics, computer science, engineering, statistical mechanics, biology, image processing, signal processing, social network modeling, biomedical modeling, machine learning and artificial intelligence. They help lay many of the foundations of statistics and mathematical finance.

Sometimes, the current popularity and importance of probability is taken for granted. However, mainstream journals dedicated to probability are relatively new. Perhaps the first significant journal dedicated to probability was the Russian journal Teoriya Veroyatnostei i ee Primeneniya, now published in English under the title Theory of Probability and Its Applications. It was first published in 1956. Other significant dedicated journals that followed relatively soon include the Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete, now Probability Theory and Related Fields in 1962, the Journal of Applied Probability in 1964, the Annals of Probability in 1973, and Stochastic Processes and Their Applications, also introduced in 1973. Now, there are over thirty high-quality venues used to publish work on probability and stochastic processes, with this number constantly increasing. Indeed, probability and stochastic processes were recognized as their own area of mathematics rather late, and one should ask how much further behind we would be without this heroic period of mathematical probability theory. An equally important question, looking ahead towards the next decade and its likely scientific and technological developments, is how much more growth should probability and stochastic processes undergo. This Special Issue is dedicated to help ensure that this growth is robust.

Prof. Dr. Michael A. Kouritzin
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

• probability
• stochastic processes
• mathematical foundations
• new trends in probability
• contemporary and future applications