Abstract/Details

Processus de diffusion: Outils de modélisation, de prévision et de contrôle

Labib, Richard.  Ecole Polytechnique, Montreal (Canada). ProQuest Dissertations Publishing, 2000. NQ53536.

Abstract (summary)

Diffusion processes defined by systems of stochastic differential equations are considered to model, forecast and control different physical phenomena.

We begin by generalizing optimal control problems for wear models of a machine by considering a performance criterion that takes the risk sensitivity of the optimizer into account. The optimal control is obtained for two and three-dimensional models from a mathematical expectation for a related uncontrolled process. Explicit solutions are presented.

Next, in order to forecast drainage basin runoff, mathematical models involving diffusion processes are tested against hydrological data obtained from the hydrographic basin of the Saguenay-Lac-St-Jean, located in northeastern Quebec. An integrated Ornstein-Uhlenbeck process is found to give better results than a deterministic model presently in use for one-day ahead estimates.

Finally, we investigate the validity of a new structure for a single neuron, that will eventually be used in multilayer neural networks to perform nonlinear pattern recognition. This new architecture is inspired by biological assumptions involving diffusion processes. It is clearly established that only six parameters are sufficient to solve the XOR problem.

Indexing (details)


Subject
Mathematics
Classification
0405: Mathematics
Identifier / keyword
Pure sciences; Diffusion; Drainage basin runoff; French and English text; Neurons; Optimal control; Stochastic differential equations
Title
Processus de diffusion: Outils de modélisation, de prévision et de contrôle
Author
Labib, Richard
Number of pages
107
Degree date
2000
School code
1105
Source
DAI-B 61/11, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
978-0-612-53536-7
Advisor
Lefebvre, Mario
University/institution
Ecole Polytechnique, Montreal (Canada)
University location
Canada
Degree
Ph.D.
Source type
Dissertation or Thesis
Language
French
Document type
Dissertation/Thesis
Dissertation/thesis number
NQ53536
ProQuest document ID
304675379
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
https://www.proquest.com/docview/304675379