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Necessary conditions for optimality for a diffusion with a non-smooth drift. (English) Zbl 0651.93077

A maximum principle for a stochastic control problem \(dx_ t=f(t,x_ t,u_ t)dt+\sigma (t,x_ t)dB_ t\), \(x(0)=x\), \(J(u)=E_ x[g(x_ T)]\), with non-smooth drift is established by approximating this problem by differentiable problems. In this way Kushner’s maximum principle is generalized and the adjoint process is characterized.
Reviewer: M.Kohlmann

MSC:

93E20 Optimal stochastic control
49K45 Optimality conditions for problems involving randomness
60J60 Diffusion processes
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
93C10 Nonlinear systems in control theory
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