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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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