We develop three important and prospective research directions that have numerous applications in (tele)communications, engineering, physics, biology, economics, transport, etc.

Direction 1. Stability and optimisation problems in complex stochastic processes.
Stability is the ability of a system to act predictably, which guarantees the quality of service for the user. In particular, serious problems may occur in the world if a significant proporsion of communication networks becomes unstable. Stability is very important in many other networks – for example, in the energy networks under uncertainty (due to use of renewables), where the management has to be organised in a way to avoid undesirable effects, like the energy collapses in the Northeastern USA and the West of England in the early 2000s.

Direction 2. Asymptotic behavior of distributions of random walks when the classical assumptions are violated.
We develop new methods and approaches to the study of random walks having complex structure and in many dimensions, with practical applications.

Direction 3. Asymptotics of rare events probabilities in complex stochastic models
The importance of this area of research has increased after the economic crisis, as it became more apparent that there is need to estimate the probabilities of rare events like the bankruptcies of companies and banks, failures in nuclear and conventional power plants, failures in computer networks and airports, and the probabilities of other potentially catastrophic events. It is known that the main cause for the occurrence of a rare event differs in the processes with “light” and with “heavy” distributions of “tails”. In the former case, there is a long period of atypical behavior of the studied process before the ruin, while in the latter case the ruin results from a single or small number of unusual events which is very difficult to predict. The Lab studies a number of difficult open problems related to the asymptotics of probabilities of rare events, in the cases of light and heavy distribution tails, with special emphasis on the latter. This requires introduction of new ideas, development of new theoretical methods and, in particular, analysis of conditions for “the principle of one big jump” to hold.

The applied probability laboratory works in close collaboration with many foreign colleagues and, in particular, with the partner “Stochastic Systems Laboratory” at Heriot-Watt University and the Maxwell Institute, Edinburgh. Researchers from Novosibirsk probability school are well-known for their achievements in developing and applying various methods and approaches to the study of complex classical probability problems and for their generalizations, while their collaborators have developed methods and approaches to the study of new mathematically complex problems that came from applications. In the presence of regular international contacts, this leads to qualitatively new opportunities for mutually beneficial joint work at the edge of scientific interests of Novosibirsk and foreign reearchers.

International partners of the laboratory: Heriot-Watt University (Edinburgh, Great Britain), Eindhoven University of Technology and University of Twente (Netherlands), University of Manchester (Great Britain), Lancaster University (Great Britain), University of Augsburg (Germany), INRIA (France), Tokyo Science University (Japan), Aarhus University (Denmark), Gothenburg University (Sweden), Soochow University, Suzhou and Nankai University Tianjin (China).

Scientific supervisor of the laboratory – Professor Sergey Foss (University of Heriot-Watt, UK)

Expert of the division – Doctor of Physics and Mathematics, Alexander Sakhanenko aisakh@mail.ru

Department of probability theory and mathematical statistics
Sobolev Institute of Mathematics, Siberian Branch of th Russian Academy of Sciences