Abstract
Original language  English 

Qualification  Doctor of Philosophy 
Awarding Institution 

Supervisors/Advisors 

Award date  22 Sep 2008 
Place of Publication  Amsterdam 
Publisher  
Print ISBNs  9789051709056 
Publication status  Published  2008 
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Measurevalued differentiation for finite products of measures : theory and applications. / Leahu, H.
Amsterdam : Vrije Universiteit Amsterdam, 2008.Research output: Thesis › Phd Thesis 4 Research NOT TU/e / Graduation NOT TU/e)
TY  THES
T1  Measurevalued differentiation for finite products of measures : theory and applications
AU  Leahu, H.
PY  2008
Y1  2008
N2  In this dissertation we perform a comprehensive analysis of measurevalued differentiation, in which weak differentiation of parameterdependent probability measures plays a central role. We develop a theory of weak differentiation of measures and show that classical concepts such as differential calculus and analyticity extend to measurevalued mappings in some appropriate sense. Concurrently, we develop applications in the area of gradient estimation, perturbation analysis and Taylor series approximations for performance measures of complex stochastic systems. The key observation is that the weak derivative of some probability measure can be represented as the rescaled difference between two probability measures, which leads to efficient simulating algorithms. More specifically, we show how weak derivatives can be used to construct (asymptotically) unbiased estimators for stochastic gradients or functional dependence of the performance measures of some stochastic systems, e.g., queueing networks or stochastic activity networks, with respect to some intrinsic parameter of the system. Eventually, we illustrate how weak derivatives can be used to derive Lipschitz constants for measurevalued mappings, which prove to be useful in performing perturbation analysis for the systems under consideration. A remarkable result shows that the stationary distribution of the waiting times in a G/G/1 queue is normcontinuous, with respect to some appropriate norm on the space of measures, provided that the service time distribution is weakly differentiable.
AB  In this dissertation we perform a comprehensive analysis of measurevalued differentiation, in which weak differentiation of parameterdependent probability measures plays a central role. We develop a theory of weak differentiation of measures and show that classical concepts such as differential calculus and analyticity extend to measurevalued mappings in some appropriate sense. Concurrently, we develop applications in the area of gradient estimation, perturbation analysis and Taylor series approximations for performance measures of complex stochastic systems. The key observation is that the weak derivative of some probability measure can be represented as the rescaled difference between two probability measures, which leads to efficient simulating algorithms. More specifically, we show how weak derivatives can be used to construct (asymptotically) unbiased estimators for stochastic gradients or functional dependence of the performance measures of some stochastic systems, e.g., queueing networks or stochastic activity networks, with respect to some intrinsic parameter of the system. Eventually, we illustrate how weak derivatives can be used to derive Lipschitz constants for measurevalued mappings, which prove to be useful in performing perturbation analysis for the systems under consideration. A remarkable result shows that the stationary distribution of the waiting times in a G/G/1 queue is normcontinuous, with respect to some appropriate norm on the space of measures, provided that the service time distribution is weakly differentiable.
M3  Phd Thesis 4 Research NOT TU/e / Graduation NOT TU/e)
SN  9789051709056
PB  Vrije Universiteit Amsterdam
CY  Amsterdam
ER 