Stochastic control problems and spherical functions on symmetric spaces
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 by T. E. Duncan and H. Upmeier PDF
 Trans. Amer. Math. Soc. 347 (1995), 10831130 Request permission
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.References

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Additional Information
 © Copyright 1995 American Mathematical Society
 Journal: Trans. Amer. Math. Soc. 347 (1995), 10831130
 MSC: Primary 93E20; Secondary 43A90, 49J45, 53C35
 DOI: https://doi.org/10.1090/S00029947199512844538
 MathSciNet review: 1284453