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Title

Solvable optimal control of Brownian motion in symmetric spaces and spherical polynomials

Authors 1

Affiliations

  1. Department of Mathematics, University of Kansas, Lawrence, Kansas 66045, U.S.A.

Bibliography

  1. V. E. Benes, L. A. Shepp and H. S. Witsenhausen, Some solvable stochastic control problems, Stochastics 4 (1980), 39-83.
  2. 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.
  3. E. Cartan, Sur certaines formes riemanniennes remarquables des géométries à groupe fondamental simple, Ann. Sci. Ecole Norm. Sup. 44 (1927), 345-467.
  4. T. E. Duncan, Dynamic programming optimality criteria for stochastic systems in Riemannian manifolds, Appl. Math. Optim. 3 (1977), 191-208.
  5. T. E. Duncan, Stochastic systems in Riemannian manifolds, J. Optim. Theory Appl. 27 (1979), 399-426.
  6. T. E. Duncan, A solvable stochastic control problem in hyerbolic three space, Systems Control Lett. 8 (1987), 435-439.
  7. T. E. Duncan, A solvable stochastic control problem in spheres, in: Contemp. Math. 73, Amer. Math. Soc., 1988, 49-54
  8. T. E. Duncan, Some solvable stochastic control problems in compact symmetric spaces of rank one, in: Contemp. Math. 97 Amer. Math. Soc., 1989, 79-96.
  9. T. E. Duncan, Some solvable stochastic control problems in noncompact symmetric spaces of rank one, Stochastics and Stochastic Rep. 35 (1991), 129-142.
  10. T. E. Duncan, A solvable stochastic control problem in the hyperbolic plane, J. Math. Sys. Estim. Control 2 (1992), 445-452.
  11. T. E. Duncan, A solvable stochastic control problem in real hyperbolic three space II, Ulam Quart. 1 (1992), 13-18.
  12. T. E. Duncan and H. Upmeier, Stochastic control problems in symmetric cones and spherical functions, in: Diffusion Processes and Related Problems in Analysis I, Birkhäuser, 1990, 263-283.
  13. T. E. Duncan and H. Upmeier, Explicitly solvable stochastic control problems in symmetric spaces of higher rank, Trans. Amer. Math. Soc., to appear.
  14. J. Faraut and A. Korányi, Analysis on Symmetric Cones, to appear.
  15. W. H. Fleming and R. W. Rishel, Deterministic and Stochastic Optimal Control, Springer, New York, 1975.
  16. Harish-Chandra, Spherical functions on a semi-simple Lie group I, Amer. J. Math. 80 (1958), 241-310.
  17. U. G. Haussman, Some examples of optimal stochastic controls or: the stochastic maximum principle at work, SIAM Rev. 23 (1981), 292-307.
  18. S. Helgason, Differential Geometry, Lie Groups and Symmetric Spaces, Academic Press, New York, 1978.
  19. S. Helgason, Groups and Geometric Analysis, Academic Press, New York, 1984.
  20. I. Macdonald, Symmetric Functions and Hall Polynomials, Clarendon Press, Oxford, 1979.
  21. R. C. Merton, Optimum consumption and portfolio rules in a continuous-time model, J. Economic Theory 3 (1971), 373-413.
Banach Center Publications
1995/32/1
Export to PBN, Opens in new tab
Pages:
183-197
Main language of publication
English
Published
1995
Exact and natural sciences