Continuous Simulation, Differential Inclusions, Uncertainty, and Traveling in Time
- 1 February 2004
- journal article
- other
- Published by SAGE Publications in SIMULATION
- Vol. 80 (2) , 87-100
- https://doi.org/10.1177/0037549704042858
Abstract
Differential inclusions (DIs) represent an important extension of differential equations. The other term used for DI is differential equations with a set-valued right-hand side. This tool can be used when the model reveals uncertainty that is given in terms of limits or permissible sets rather than random variables. A model of stock exchange dynamics with uncertain information and a model with an ideal predictor are presented to illustrate possible applications. The ideal predictor problem is equivalent to the problem of passing the information from the future to the present, or traveling into the past to use the present information and change the model trajectory. It is shown that the uncertainty over the future can be simulated using differential inclusions. A differential inclusion solver is described.Keywords
This publication has 6 references indexed in Scilit:
- The Dynamics of Long-Range Financial Accumulation and CrisisNonlinear Dynamics, Psychology, and Life Sciences, 1999
- Some remarks on nonconvex optimal controlJournal of Mathematical Analysis and Applications, 1986
- Differential InclusionsPublished by Springer Nature ,1984
- On some generalization of “bang-bang” controlJournal of Mathematical Analysis and Applications, 1984
- Fuzzy setsInformation and Control, 1965
- Sur les champs de demi-droites et les équations différentielles du premier ordreBulletin de la Société Mathématiques de France, 1934