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Stochastic control problems and spherical functions on symmetric spaces

Duncan, Tyrone E.
; 
Upmeier, Harald
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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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This is the published version, also available here: http://dx.doi.org/10.1090/S0002-9947-1995-1284453-8. First published in Trans. Amer. Math. Soc. in 1995, published by the American Mathematical Society.
Date
1995-01-01
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American Mathematical Society
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Mathematics Scholarly Works
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DuncanTE_April1995.pdf
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Duncan, Tyrone E. "Stochastic control problems and spherical functions on symmetric spaces." Trans. Amer. Math. Soc. (1995) 347. 1083-1130. http://dx.doi.org/10.1090/S0002-9947-1995-1284453-8
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https://hdl.handle.net/1808/16691
DOI
10.1090/S0002-9947-1995-1284453-8
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