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

T. Duncan

Banach Center Publications (1995)

  • Volume: 32, Issue: 1, page 183-197
  • ISSN: 0137-6934

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Duncan, T.. "Solvable optimal control of Brownian motion in symmetric spaces and spherical polynomials." Banach Center Publications 32.1 (1995): 183-197. <http://eudml.org/doc/262592>.

@article{Duncan1995,
author = {Duncan, T.},
journal = {Banach Center Publications},
keywords = {stochastic control problems; diffusion on manifolds; symmetric spaces; Brownian motion; Laplace-Beltrami operator; optimal control},
language = {eng},
number = {1},
pages = {183-197},
title = {Solvable optimal control of Brownian motion in symmetric spaces and spherical polynomials},
url = {http://eudml.org/doc/262592},
volume = {32},
year = {1995},
}

TY - JOUR
AU - Duncan, T.
TI - Solvable optimal control of Brownian motion in symmetric spaces and spherical polynomials
JO - Banach Center Publications
PY - 1995
VL - 32
IS - 1
SP - 183
EP - 197
LA - eng
KW - stochastic control problems; diffusion on manifolds; symmetric spaces; Brownian motion; Laplace-Beltrami operator; optimal control
UR - http://eudml.org/doc/262592
ER -

References

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  1. [1] V. E. Benes, L. A. Shepp and H. S. Witsenhausen, Some solvable stochastic control problems, Stochastics 4 (1980), 39-83. Zbl0451.93068
  2. [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. Zbl0574.93067
  3. [3] E. Cartan, Sur certaines formes riemanniennes remarquables des géométries à groupe fondamental simple, Ann. Sci. Ecole Norm. Sup. 44 (1927), 345-467. Zbl53.0393.01
  4. [4] T. E. Duncan, Dynamic programming optimality criteria for stochastic systems in Riemannian manifolds, Appl. Math. Optim. 3 (1977), 191-208. Zbl0403.49025
  5. [5] T. E. Duncan, Stochastic systems in Riemannian manifolds, J. Optim. Theory Appl. 27 (1979), 399-426. Zbl0377.93072
  6. [6] T. E. Duncan, A solvable stochastic control problem in hyerbolic three space, Systems Control Lett. 8 (1987), 435-439. Zbl0624.93077
  7. [7] T. E. Duncan, A solvable stochastic control problem in spheres, in: Contemp. Math. 73, Amer. Math. Soc., 1988, 49-54 Zbl0657.93079
  8. [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. [9] T. E. Duncan, Some solvable stochastic control problems in noncompact symmetric spaces of rank one, Stochastics and Stochastic Rep. 35 (1991), 129-142. Zbl0728.60081
  10. [10] T. E. Duncan, A solvable stochastic control problem in the hyperbolic plane, J. Math. Sys. Estim. Control 2 (1992), 445-452. 
  11. [11] T. E. Duncan, A solvable stochastic control problem in real hyperbolic three space II, Ulam Quart. 1 (1992), 13-18. 
  12. [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. Zbl0725.93086
  13. [13] T. E. Duncan and H. Upmeier, Explicitly solvable stochastic control problems in symmetric spaces of higher rank, Trans. Amer. Math. Soc., to appear. Zbl0850.93887
  14. [14] J. Faraut and A. Korányi, Analysis on Symmetric Cones, to appear. Zbl0841.43002
  15. [15] W. H. Fleming and R. W. Rishel, Deterministic and Stochastic Optimal Control, Springer, New York, 1975. 
  16. [16] Harish-Chandra, Spherical functions on a semi-simple Lie group I, Amer. J. Math. 80 (1958), 241-310. 
  17. [17] U. G. Haussman, Some examples of optimal stochastic controls or: the stochastic maximum principle at work, SIAM Rev. 23 (1981), 292-307. 
  18. [18] S. Helgason, Differential Geometry, Lie Groups and Symmetric Spaces, Academic Press, New York, 1978. Zbl0451.53038
  19. [19] S. Helgason, Groups and Geometric Analysis, Academic Press, New York, 1984. Zbl0543.58001
  20. [20] I. Macdonald, Symmetric Functions and Hall Polynomials, Clarendon Press, Oxford, 1979. 
  21. [21] R. C. Merton, Optimum consumption and portfolio rules in a continuous-time model, J. Economic Theory 3 (1971), 373-413. Zbl1011.91502

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