Stochastic maximum principle for distributed parameter systems. (English) Zbl 0519.93042


93C20 Control/observation systems governed by partial differential equations
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
93E20 Optimal stochastic control
35R60 PDEs with randomness, stochastic partial differential equations
49K20 Optimality conditions for problems involving partial differential equations
49K45 Optimality conditions for problems involving randomness
Full Text: DOI


[1] Kushner, H.J., Necessary conditions for continuous parameter stochastic optimization problems, SIAM J. control, Vol. 10, 550-565, (1972) · Zbl 0242.93063
[2] Kushner, H.J., On the optimal control of a system governed by a linear parabolic equation with white noise inputs, SIAM J. control, Vol. 6, 596-614, (1968) · Zbl 0186.23404
[3] Bismut, J.M., Analyse convexe et probabilités, (1973), Thesé, Paris
[4] Bismut, J.M., An introductory approach to duality in optimal stochastic control, SIAM rev., Vol. 20, No. 1, (January 1978)
[5] Bensoussan, A., Contrôle optimal stochastique de systémes gouvernés par des équations aux dérivées partielles, Rendi conti di matematica, (1969), Rome · Zbl 0249.93058
[6] Bensoussan, A., Control of stochastic partial differential equations, () · Zbl 0548.35037
[7] Bensoussan, A., Lectures on stochastic control, CIME course on stochastic control and filtering, (July 1981), Cortona
[8] Bensoussan, A.; Viot, M., Optimal control of stochastic linear distributed parameter systems, SIAM J. control, Vol. 13, No. 4, (July 1975)
[9] Kunita, H.; Watanabe, S., On square integrable martingales, Nagoya math. journal, Vol. 30, (August 1967)
[10] Lions, J.L., Contrôle optimal de systémes distribués, (1968), Springer Dunod, Paris, English translation by S.K. Mitter · Zbl 0278.49004
[11] Pardoux, E., Stochastic partial differential equations and filtering of diffusion processes, Stochastics, Vol. 3, 127-167, (1979) · Zbl 0424.60067
[12] Tartar, L., Sur l’étude directe d’équations non linéaires intervenant en théorie du contrôle optimal, J. funct. anal., Vol. 17, 1-47, (1974) · Zbl 0293.49004
[13] Wonham, W.M., On a matrix Riccati equation of stochastic control, SIAM J. control, Vol. 6, 312-326, (1968) · Zbl 0164.19101
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.