Ebook: Dynamic Probabilistic Models and Social Structure: Essays on Socioeconomic Continuity
Author: Guillermo L. Gómez M. (auth.)
- Tags: Probability Theory and Stochastic Processes, Systems Theory Control, Economics general, Theoretical Mathematical and Computational Physics
- Series: Theory and Decision Library 19
- Year: 1992
- Publisher: Springer Netherlands
- Edition: 1
- Language: English
- pdf
Mathematical models have been very successful in the study of the physical world. Galilei and Newton introduced point particles moving without friction under the action of simple forces as the basis for the description of concrete motions like the ones of the planets. This approach was sustained by appro priate mathematical methods, namely infinitesimal calculus, which was being developed at that time. In this way classical analytical mechanics was able to establish some general results, gaining insight through explicit solution of some simple cases and developing various methods of approximation for handling more complicated ones. Special relativity theory can be seen as an extension of this kind of modelling. In the study of electromagnetic phenomena and in general relativity another mathematical model is used, in which the concept of classical field plays the fundamental role. The equations of motion here are partial differential equations, and the methods of study used involve further developments of classical analysis. These models are deterministic in nature. However it was realized already in the second half of last century, through the work of Maxwell, Boltzmann, Gibbs and others, that in the discussion of systems involving a great number of particles, the deterministic description is not by itself of great help, in particu lar a suitable "weighting" of all possible initial conditions should be considered.
Content:
Front Matter....Pages i-xiv
Front Matter....Pages 1-2
Introduction and outline....Pages 3-57
Towards a working model and goal setting....Pages 59-116
Change and time in development and growth processes....Pages 117-169
Front Matter....Pages 171-172
Stopping times and other probabilistic issues....Pages 173-215
The martingale tuning of driving forces....Pages 217-277
Interacting goals in a variational guise....Pages 279-346
Front Matter....Pages 347-348
Essentials on systems and control....Pages 349-364
Semimartingale calculus....Pages 365-399
Stochastic control theory....Pages 401-419
Back Matter....Pages 421-450
Content:
Front Matter....Pages i-xiv
Front Matter....Pages 1-2
Introduction and outline....Pages 3-57
Towards a working model and goal setting....Pages 59-116
Change and time in development and growth processes....Pages 117-169
Front Matter....Pages 171-172
Stopping times and other probabilistic issues....Pages 173-215
The martingale tuning of driving forces....Pages 217-277
Interacting goals in a variational guise....Pages 279-346
Front Matter....Pages 347-348
Essentials on systems and control....Pages 349-364
Semimartingale calculus....Pages 365-399
Stochastic control theory....Pages 401-419
Back Matter....Pages 421-450
....