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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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), 1083-1130 Request permission


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
  • © Copyright 1995 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 347 (1995), 1083-1130
  • MSC: Primary 93E20; Secondary 43A90, 49J45, 53C35
  • DOI:
  • MathSciNet review: 1284453