Actions on Environment under uncertaintystochastic formulation and the associated deterministic problem

  1. Jesús Ildefonso Díaz Díaz
  2. Ch. Faghloumi
Journal:
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas ( RACSAM )

ISSN: 1578-7303

Year of publication: 2008

Volume: 102

Issue: 2

Pages: 335-353

Type: Article

DOI: 10.1007/BF03191827 DIALNET GOOGLE SCHOLAR lock_openOpen access editor

More publications in: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas ( RACSAM )

Abstract

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.