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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

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
Full Text: DOI
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