- Classical general and constructive theory of Markov processes, including classification criteria, convergence rates etc.
- Global and local properties of trajectories of random walks
- Diffusion and jump processes
- Random media
- General theory of Markov and Gibbs random fields
- General theory of processes with local interactions and infinite particle systems
- Equilibrium and non-equilibrium statistical physics, quantum field theory
- Scaling for large Markov processes, such as fluid models for finite-dimensional queueing systems, hydrodynamics for particle systems, diffusion approximations for queueing networks, etc.
- Simulated annealing, genetic algorithms
- Markovian aspects of neural nets
- Analytic and algebraic geometry methods related to Markov processes
- Telecommunications and computer networks
- Controlled Markov processes and decision processes
- Simulation of large Markov chains and Monte Carlo methods

Additionally, the Journal focuses on mathematical modelling of today's enormous wealth of problems from modern technology, like artificial intelligence, large scale networks, data bases, parallel simulation, computer architectures, etc.

Research papers, reviews, tutorial papers and additionally short explanations of new applied fields and new mathematical problems in the above fields are welcome.

The journal is abstracted/indexed in: Mathematical Reviews, Science Citation Index-Expanded (SCIE) including the Web of Science, ISI Alerting Service, Current Contents/Physical, Chemical and Earth Scienses (CC/PC&ES), Zentralblatt Math.