Calculus of Variations on Time Scales and Its Applications to Economics
The goal of time scale research is to progress the development of a harmonized theory that is all encompassing of the more commonly known specialized forms. The main results of this paper is the presentation of the Ramsey model which can be written using both the A and V operators, and solved using the two separate theories of the calculus of variations on time scales. The next presentation will be of the solution of an adjustment model, for a specific form of a time scale, whose functional can only be optimized, using the existing theory, when written with the A operator. We will also develop certain elements of stochastic time scale calculus, in order to lay the groundwork necessary to develop the theory of stochastic calculus of variations on time scales.
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