Menaldi, José Luis; Robin, Maurice 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 Cited in 1 Document 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 Keywords:stochastic differential equation with jumps; cheap control; monotone follower; value function; nonlinear semigroup; Hamilton-Jacobi-Bellman equation Citations:Zbl 0547.00029; Zbl 0554.93076 PDFBibTeX XML