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作者：HAUSSMANN, UG
摘要：The quadratic variation of Brownian motion is used to give a new definition of a generalized Hessian for nonsmooth functions, totally independently of any gradients. A calculus is developed for the generalized Hessian of functions whose gradient is Lipschitz. It is also shown that for convex functions the Hessian is nonempty.
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作者：FEINBERG, EA
作者单位：Yale University
摘要：We consider a discrete time Markov decision model with Borel state and action spaces. It is proved that the supremum of the expected total rewards under all randomized stationary strategies is equal to the supremum of these rewards under all (nonrandomized) stationary strategies.
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作者：HORVATH, L
摘要：We consider a queueing system with one or more stations. We show that the queue length processes can be approximated with Brownian motions or reflected Brownian motions. Using the approximations we obtain rates of convergence of the distributions and expected values of queue lengths.
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作者：SCHAL, M
摘要：For a semi-Markov decision model with average return, the validity of the second optimality equation is shown in the (nonmodified) form where the actions run through the set of all admissible actions rather than through the set of maximum points (conserving actions) for the first optimality equation. As a consequence the existence of a strongly optimal stationary policy is shown. The results seem to be known only for finite state finite action models whereas here countable state compact action...
