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V. E. Benes, L. A. Shepp and H. S. Witsenhausen, Some solvable stochastic control problems, Stochastics 4(1980), 39–83.
A. Bensoussan and J. H. Van Schuppen, Optimal control of partially observable stochastic systems with an exponential-of-integral performance index, SIAM J. Control Optim. 23(1985), 599–613.
F. A. Berezin, Doklady Akad. Nauk SSR N.S. 107 (1956), 9–12 and 110 (1956), 897–900.
T. E. Duncan, Some stochastic systems on manifolds, Lecture Notes in Econ. and Math. Systems 107(1975), 262–270, Springer-Verlag, New York.
T. E. Duncan, Dynamic programming optimality criteria for stochastic systems in Riemannian manifolds, Appl. Math. Optim. 3(1977), 191–208.
T. E. Duncan, Stochastic systems in Riemannian manifolds, J. Optimization Theory Appl. 27(1979), 399–426.
T. E. Duncan, A solvable stochastic control problem in hyperbolic three space, Systems and Control Letters, 8(1987), 435–439.
T. E. Duncan, A solvable stochastic control problem in spheres in Geometry of Random Motion (R. Durrett and M. Pinsky, eds.) Contemporary Mathematics, 73(1988), 49–54, Amer. Math. Soc., Providence.
T. E. Duncan, Some solvable stochastic control problems in compact symmetric spaces of rank one, to appear in Contemporary Mathematics.
T. E. Duncan, Some solvable stochastic control problems in noncompact symmetric spaces of rank one, to appear in Stochastics.
W. H. Fleming and R. W. Rishel, Deterministic and Stochastic Optimal Control, Springer-Verlag, 1975.
Harish-Chandra, Spherical functions on a semi-simple Lie group I., Amer. J. Math. 80(1958), 241–310.
U. G. Haussmann, Some examples of optimal stochastic controls or: the stochastic maximum principle at work, SIAM Review 23(1981), 292–307.
S. Helgason, Differential Geometry, Lie Groups and Symmetric Spaces, Academic Press, 1978.
S. Helgason, Groups and Geometric Analysis, Academic Press, 1984.
N. Ikeda and S. Watanabe, Stochastic Differential Equations and Diffusion Processes, North-Holland, 1981.
K. Itô and H. P. McKean, Jr., Diffusion Processes and Their Sample Paths, Springer-Verlag, 1965.
R. C. Merton, Optimum consumption and portfolio rules in a continuous-time model, J. Economic Theory 3(1971), 373–413.
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© 1989 Springer-Verlag
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Duncan, T.E. (1989). Some solvable stochastic control problems in symmetric spaces of type IV. In: Zabczyk, J. (eds) Stochastic Systems and Optimization. Lecture Notes in Control and Information Sciences, vol 136. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0002689
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DOI: https://doi.org/10.1007/BFb0002689
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