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An evolutionary monotone follower problem in [0, 1]
Published online by Cambridge University Press: 17 February 2009
Abstract
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We consider in this article an evolutionary monotone follower problem in [0,1]. State processes under consideration are controlled diffusion processes 
, solutions of dyx(t) = g(yx(t), t)dt + σu(yx(t), t) dwt + dυt with yx(0) = x ∈[0, 1], where the control processes υt are increasing, positive, and adapted. The cost functional is of integral type, with certain explicit cost of control action including the cost of jumps. We shall present some analytic results of the value function, mainly its characterisation, by standard dynamic programming arguments.
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- Copyright © Australian Mathematical Society 1989
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