Stochastic control problems and spherical functions on symmetric spaces

Authors:
T. E. Duncan and H. Upmeier

Journal:
Trans. Amer. Math. Soc. **347** (1995), 1083-1130

MSC:
Primary 93E20; Secondary 43A90, 49J45, 53C35

DOI:
https://doi.org/10.1090/S0002-9947-1995-1284453-8

MathSciNet review:
1284453

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Abstract | References | Similar Articles | Additional Information

Abstract: A family of explicitly solvable stochastic control problems is formulated and solved in noncompact symmetric spaces. The symmetric spaces include all of the classical spaces and four of the exceptional spaces. The stochastic control problems are the control of Brownian motion in these symmetric spaces by a drift vector field. For each symmetric space a family of stochastic control problems is formulated by using spherical functions in the cost functionals. These spherical functions are explicitly described and are polynomials in suitable coordinates. A generalization to abstract root systems is given.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1995-1284453-8

Keywords:
Stochastic control,
spherical functions,
controlled diffusions in symmetric spaces,
Laplace-Beltrami operator,
explicitly solvable control problems

Article copyright:
© Copyright 1995
American Mathematical Society