Approximation of hypergeometric functions with matricial argument through their development in series of zonal polynomials.
On the existence and uniqueness of the solution processes in McShane's stochastic integral equation systems
Parametric dependence of the solution processes on the coefficients in McShane's stochastic integral equation systems
Uniqueness of optimal policies as a generic property of discounted Markov decision processes: Ekeland's variational principle approach
Many examples in optimization, ranging from Linear Programming to Markov Decision Processes (MDPs), present more than one optimal solution. The study of this non-uniqueness is of great mathematical interest. In this paper the authors show that in a specific family of discounted MDPs, non-uniqueness is a “fragile” property through Ekeland's Principle for each problem with at least two optimal policies; a perturbed model is produced with a unique optimal policy. This result not only supersedes previous...
An extended version of average Markov decision processes on discrete spaces under fuzzy environment
The article presents an extension of the theory of standard Markov decision processes on discrete spaces and with the average cost as the objective function which permits to take into account a fuzzy average cost of a trapezoidal type. In this context, the fuzzy optimal control problem is considered with respect to two cases: the max-order of the fuzzy numbers and the average ranking order of the trapezoidal fuzzy numbers. Each of these cases extends the standard optimal control problem, and for...
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