×

Some control problems of degenerate diffusions with unbounded cost. (English) Zbl 0565.93069

Recent mathematical methods in dynamic programming, Proc. Conf., Rome/Italy 1984, Lect. Notes Math. 1119, 113-138 (1985).
[For the entire collection see Zbl 0547.00029.]
The paper treats the following control problems: the system is governed by a stochastic differential equation with jumps and a control modifies the system by adding an adapted process with locally bounded variation. This is a generalization of cheap control problems and monotone follower problems. The authors characterize the value function from various points of view, i.e. nonlinear semigroup, Hamilton-Jacobi-Bellman equation and variational formulation. Most of the results are extensions of previous ones by the same authors [cf. e.g. IEEE Trans. Autom. Control AC-29, 991- 1004 (1984; Zbl 0554.93076)].
Reviewer: M.Nisio

MSC:

93E20 Optimal stochastic control
49J40 Variational inequalities
49L20 Dynamic programming in optimal control and differential games
45K05 Integro-partial differential equations
49J55 Existence of optimal solutions to problems involving randomness
60J75 Jump processes (MSC2010)
47H20 Semigroups of nonlinear operators