论文信息 - Controlled diffusion processes on infinite horizon with the overtaking criterion

Controlled diffusion processes on infinite horizon with the overtaking criterion

The optimal control of diffusion processes on the infinite time interval are studied. All the costs diverge to infinity and we employ the overtaking criterion, as well as considering minimal growth rate controls. The Bellman equation for the problem is considered and its solution is given an interpretation connected with the overtaking optimality notion. Control problems with a cost including a generalized discount factor (which is not integrable on [(, ∞)) are also studied. Both cases, where the diffusion is inRn or where it is reflected from the boundary of a bounded set, are considered.

Arie Leizarowitz

[1] Alain Bensoussan,et al. Impulse Control and Quasi-Variational Inequalities , 1984 .

[2] S. Varadhan,et al. Diffusion processes with boundary conditions , 1971 .

[3] von Weizäscker,et al. Existence of Optimal Programs of Accumulation for an Infinite Time Horizon , 1965 .

[4] R. Khasminskii. Stochastic Stability of Differential Equations , 1980 .

[5] Z. Artstein,et al. Tracking periodic signals with the overtaking criterion , 1985 .

[6] Construction and control of reflected diffusion with jumps , 1985 .

[7] Shinzo Watanabe,et al. On stochastic differential equations for multi-dimensional diffusion processes with boundary conditions II , 1971 .

[8] Arie Leizarowitz,et al. Existence of Overtaking Optimal Trajectories for Problems with Convex Integrands , 1985, Math. Oper. Res..

[9] P. Lions,et al. Stochastic differential equations with reflecting boundary conditions , 1984 .

[10] M. Robin. Long-term average cost control problems for continuous time Markov processes: A survey , 1983 .

[11] D. Gale. On Optimal Development in a Multi-Sector Economy , 1967 .

[12] A. Leizarowitz. Infinite horizon stochastic regulation and tracking with the overtaking criterion , 1987 .

[13] P. Lions,et al. Linear oblique derivative problems for the uniformly elliptic Hamilton-Jacobi-Bellman equation , 1986 .