Diffusion approximations for controlled weakly interacting large finite state systems with simultaneous jumps
| Autor: | Eric Friedlander, Amarjit Budhiraja |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Statistics and Probability
propagation of chaos Markov process 01 natural sciences 010104 statistics & probability symbols.namesake 60J28 stochastic networks Bellman equation 60K25 FOS: Mathematics 60K35 60H30 93E20 (Primary) 60J28 60J70 60K25 91B70 (Secondary) stochastic control Limit (mathematics) Statistical physics 0101 mathematics Diffusion (business) Mathematics rate control Stochastic control 010102 general mathematics Degenerate energy levels Probability (math.PR) 93E20 State (functional analysis) Mean field approximations Asymptotically optimal algorithm 91B70 60K35 asymptotic optimality symbols Statistics Probability and Uncertainty 60H30 Mathematics - Probability ad hoc wireless networks 60J70 diffusion approximations |
| Zdroj: | Ann. Appl. Probab. 28, no. 1 (2018), 204-249 |
| Popis: | We consider a rate control problem for an $N$-particle weakly interacting finite state Markov process. The process models the state evolution of a large collection of particles and allows for multiple particles to change state simultaneously. Such models have been proposed for large communication systems (e.g. ad hoc wireless networks) but are also suitable for other settings such as chemical-reaction networks. An associated diffusion control problem is presented and we show that the value function of the $N$-particle controlled system converges to the value function of the limit diffusion control problem as $N\to\infty$. The diffusion coefficient in the limit model is typically degenerate, however under suitable conditions there is an equivalent formulation in terms of a controlled diffusion with a uniformly non-degenerate diffusion coefficient. Using this equivalence, we show that near optimal continuous feedback controls exist for the diffusion control problem. We then construct near asymptotically optimal control policies for the $N$-particle system based on such continuous feedback controls. Results from some numerical experiments are presented. Comment: 41 Pages |
| Databáze: | OpenAIRE |
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