Actions on Environment under uncertaintystochastic formulation and the associated deterministic problem
- Jesús Ildefonso Díaz Díaz
- Ch. Faghloumi
ISSN: 1578-7303
Any de publicació: 2008
Volum: 102
Número: 2
Pàgines: 335-353
Tipus: Article
Altres publicacions en: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas ( RACSAM )
Resum
An application of the results of this paper proves that there is not always an economic benefit when destroying the environment for planting an alternative industrial project. Our criterion, to act, to delay or to deny the industrial investment over the environment, is given in terms of the free boundary associated to a deterministic degenerate obstacle problem (on an unbounded domain) associated to the stochastic optimal control problem formulated, initially, in terms of some suitable stochastic diffusion processes. The localizing estimates on the free boundary are obtained through a suitable spatial change of variables and by working with a suitable distance associated to the coefficient of the elliptic operator.