We consider a class of stochastic control problems where uncertainty is due to driving noises of general nature as well as to rapidly fluctuating processes affecting the drift. We show that, when the noise ”intensity” is small and the fluctuations become fast, the stochastic problems can be approximated by a deterministic one. We also show that the optimal control of the deterministic problem i...

We study stochastic delay differential equations (SDDE) where the coefficients depend on the moving averages of the state process. As a first contribution, we provide sufficient conditions under which the solution of the SDDE and a linear path functional of it admit a finite-dimensional Markovian representation. As a second contribution, we show how approximate finite-dimensional Markovian repr...

Pontryagin's principle is used to study the shape of the supersonic part of the nozzle of a carbon dioxide gas-dynamic laser whose gain is maximal. The exact shape is obtained for the uncoupled approximation of Anderson's bimodal model. In this case, if sharp corners are allowed, the ceiling of the supersonic part consists of a slant rectangular sheet followed by a horizontal one; otherwise...