Controlled Nonlinear Stochastic Delay Equations: Part II: Approximations and Pipe-Flow Representations

Controlled Nonlinear Stochastic Delay Equations: Part II: Approximations and Pipe-Flow... This is the second part of a work dealing with key issues that have not been addressed in the modeling and numerical optimization of nonlinear stochastic delay systems. We consider new classes of models, such as those with nonlinear functions of several controls (such as products), each with is own delay, controlled random Poisson measure driving terms, admissions control with delayed retrials, and others. Part I was concerned with issues concerning the class of admissible controls and their approximations, since the classical definitions are inadequate for our models. This part is concerned with transportation equation representations and their approximations. Such representations of nonlinear stochastic delay models have been crucial in the development of numerical algorithms with much reduced memory and computational requirements. The representations for the new models are not obvious and are developed. They also provide a template for the adaptation of the Markov chain approximation numerical methods. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

Controlled Nonlinear Stochastic Delay Equations: Part II: Approximations and Pipe-Flow Representations

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Publisher
Springer Journals
Copyright
Copyright © 2012 by Springer Science+Business Media, LLC
Subject
Mathematics; Mathematical Methods in Physics; Calculus of Variations and Optimal Control; Optimization; Numerical and Computational Physics; Theoretical, Mathematical and Computational Physics; Systems Theory, Control
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s00245-012-9164-2
Publisher site
See Article on Publisher Site

Abstract

This is the second part of a work dealing with key issues that have not been addressed in the modeling and numerical optimization of nonlinear stochastic delay systems. We consider new classes of models, such as those with nonlinear functions of several controls (such as products), each with is own delay, controlled random Poisson measure driving terms, admissions control with delayed retrials, and others. Part I was concerned with issues concerning the class of admissible controls and their approximations, since the classical definitions are inadequate for our models. This part is concerned with transportation equation representations and their approximations. Such representations of nonlinear stochastic delay models have been crucial in the development of numerical algorithms with much reduced memory and computational requirements. The representations for the new models are not obvious and are developed. They also provide a template for the adaptation of the Markov chain approximation numerical methods.

Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Aug 1, 2012

References

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