2012-10-13Buch DOI: 10.18452/8426
Quantitative Stability Analysis of Stochastic Generalized Equations
We consider the solution of a system of stochastic generalized equations (SGE) where theunderlying functions are mathematical expectation of random set-valued mappings. SGE hasmany applications such as characterizing optimality conditions of a nonsmooth stochastic optimization problem and a stochastic equilibrium problem. We derive quantitative continuityof expected value of the set-valued mapping with respect to the variation of the underlyingprobability measure in a metric space. This leads to the subsequent qualitative and quantitative stability analysis of solution set mappings of the SGE. Under some metric regularityconditions, we derive Aubin’s property of the solution set mapping with respect to the changeof probability measure. The established results are applied to stability analysis of stationary points of classical one stage and two stage stochastic minimization problems, two stagestochastic mathematical programs with equilibrium constraints and stochastic programs withsecond order dominance constraints.
Dateien zu dieser Publikation
Is Part Of Series: SIAM Journal on Optimization, 24, 2014
Anzeige der Publikationen mit ähnlichem Titel, Autor, Urheber und Thema.
2005-11-02BuchDelay differential equations driven by Lévy processes: stationarity and Feller properties Reiß, Markus; Riedle, Markus; Gaans, Onno vanWe consider a stochastic delay differential equation driven by a general Lévy process. Both, the drift and the noise term may depend on the past, but only the drift term is assumed to be linear. We show that the segment ...
2002-10-03BuchStability of Linear Stochastic Difference Equations in Controlled Random Environments Horst, Ulrich
2005-03-24BuchA two state model for noise-induced resonance in bistable systems with delay Fischer, Markus; Imkeller, PeterThe subject of the present paper is a simplified model for a symmetric bistable system with memory or delay, the reference model, which in the presence of noise exhibits a phenomenon similar to what is known as stochastic ...