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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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References:
[1] Arkin V. I., Soviet, Math. Dokl 20 pp 1–
[2] Bensoussan A., Non Linear filtering and stochastic Control, proc. Gortona (1981)
[3] Bismut J. M., Controle des systemes Lineaires quadratiques:application á l’integrale stochastique.Sem. proba XII
[4] Ekeland I., Amer. Math. Soc 1 pp 324– (1979)
[5] DOI: 10.1016/0022-247X(74)90025-0 · Zbl 0286.49015 · doi:10.1016/0022-247X(74)90025-0
[6] Elliott R. J., Stochastics 3 pp 229– (1980)
[7] Frankowska H., Siam Jour, on Control and Optim 22 (1984)
[8] Haussman U. G., A Stochastic Maximum Principle for Optimal Control of Diffusions (1986)
[9] Haussman U. G., The Maximum Principle of Optimal Control of Diffusions(Preprint)
[10] Jacod J., Sur un type de convergence intermediaire entre la convergence en loi et la convergence en probabilité · Zbl 0458.60016
[11] Jacod J., Weak and strong solutions of stochastic differential equations:Existence and stability, Proc. Durham (1980)
[12] DOI: 10.1137/0310041 · Zbl 0242.93063 · doi:10.1137/0310041
[13] Mezerdi B., Thése de 3emeCycle (1986)
[14] Pellaumail J., Solutions faibles et semi-martingale;Sem. proba. XV · Zbl 0468.60057
[15] DOI: 10.1016/0022-0396(75)90080-7 · Zbl 0272.49005 · doi:10.1016/0022-0396(75)90080-7
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