Analytical and numerical methods for solving stochastic dynamical decision problems
| Programmee: | Institutional Projects |
| Code: | 011302 |
| Execution period: | 2024 – 2027 |
| Institutions: | |
| Project Leader: | Capcelea Maria |
| Participants: | Mathematical Modeling |
Summary
The aim of this subprogram is to create a mathematical tool for studying and solving a new class of stochastic dynamic decision problems that extends and generalizes the discrete Markov decision processes, telegraph processes (diffusion processes), optimal control problems on dynamic networks, classical queuing theory problems and the thermo-elastic theory of solid bodies problems. The basic generalizations and elaborations of this subprogram are the following:
- Formulation and elaboration of the solution concept for the multi-criteria and the game variants of Markov decision processes controlled by several decision makes;
- Formulation of the necessary and sufficient conditions of the existence of the solutions in the sense of Pareto, Nash and Stackelberg for the multi-criteria and the game variants of Markov decision problems;
- Investigation and solving the stochastic positional games, determining the stationary Nash equilibrium and the optimal stationary strategies of the players;
- Determining the optimal stationary and nonstationary strategies for Markov decision processes with finite and infinite time horizon;
- Investigation diffusion processes in multidimensional Euclid spaces and determining the basic probabilistic characteristics for such processes;
- Elaboration and argumentation of analytical methods and numerical algorithms for determining the stationary and nonstationary strategies for the control problems on dynamic networks of large dimension.
The elaborated algorithms of the considered problems will be theoretic grounded, tested and analyzed from computational point of view. The mathematical models and analytic methods can be used for the analyses of the economic growth models, for solving practical solid body and gas mechanic problems, diffusion problems and queuing theory problems. The expected research results will be published in prestigious national and international journals and will be presented at the diverse scientific events of our country and abroad.
