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Gaussian Coarse Graining of a Master Equation Generalisation
KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA (closed 2012-06-30).
(English)Manuscript (preprint) (Other academic)
Abstract [en]

Abstract. In this report, statistical signal properties are analysed and aGaussian process model is developed for scenarios with a moving receiver ina scattering environment, as in Clarke’s model, with the generalisation thatnoise is introduced through scatterers randomly flipping on and off as a functionof time. The Gaussian process model is developed by extracting meanand covariance properties from the Multipath Fading Channel model (MFC).That is, we verify that under certain assumptions, signal realisations of theMFC model converge to a Gaussian process and thereafter compute the Gaussianprocess’ covariance matrix, which is needed to construct Gaussian processsignal realisations. The obtained Gaussian process model is, under certainassumptions, less computationally costly, contains more channel informationand has very similar signal properties to its corresponding MFC model. Theproblem of fitting our model’s flip rate and scatterer density to measured signaldata is also studied.

National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:kth:diva-12917OAI: oai:DiVA.org:kth-12917DiVA: diva2:319594
Note

QC 100518

Available from: 2010-05-18 Created: 2010-05-18 Last updated: 2013-05-14Bibliographically approved
In thesis
1. Coarse Graining Monte Carlo Methods for Wireless Channels and Stochastic Differential Equations
Open this publication in new window or tab >>Coarse Graining Monte Carlo Methods for Wireless Channels and Stochastic Differential Equations
2010 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis consists of two papers considering different aspects of stochastic process modelling and the minimisation of computational cost.

In the first paper, we analyse statistical signal properties and develop a Gaussian pro- cess model for scenarios with a moving receiver in a scattering environment, as in Clarke’s model, with the generalisation that noise is introduced through scatterers randomly flip- ping on and off as a function of time. The Gaussian process model is developed by extracting mean and covariance properties from the Multipath Fading Channel model (MFC) through coarse graining. That is, we verify that under certain assumptions, signal realisations of the MFC model converge to a Gaussian process and thereafter compute the Gaussian process’ covariance matrix, which is needed to construct Gaussian process signal realisations. The obtained Gaussian process model is under certain assumptions less computationally costly, containing more channel information and having very similar signal properties to its corresponding MFC model. We also study the problem of fitting our model’s flip rate and scatterer density to measured signal data.

The second paper generalises a multilevel Forward Euler Monte Carlo method intro- duced by Giles [1] for the approximation of expected values depending on the solution to an Ito stochastic differential equation. Giles work [1] proposed and analysed a Forward Euler Multilevel Monte Carlo method based on realsiations on a hierarchy of uniform time discretisations and a coarse graining based control variates idea to reduce the computa- tional effort required by a standard single level Forward Euler Monte Carlo method. This work introduces an adaptive hierarchy of non uniform time discretisations generated by adaptive algorithms developed by Moon et al. [3, 2]. These adaptive algorithms apply either deterministic time steps or stochastic time steps and are based on a posteriori error expansions first developed by Szepessy et al. [4]. Under sufficient regularity conditions, our numerical results, which include one case with singular drift and one with stopped dif- fusion, exhibit savings in the computational cost to achieve an accuracy of O(T ol), from O(T ol−3 ) to O (log (T ol) /T ol)2 . We also include an analysis of a simplified version of the adaptive algorithm for which we prove similar accuracy and computational cost results.

 

Place, publisher, year, edition, pages
Stockholm: KTH, 2010. viii, 20 p.
Series
Trita-CSC-A, ISSN 1653-5723 ; 2010:07
Keyword
Coarse graining, Monte Carlo Methods, Stochastic processes
National Category
Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-12897 (URN)978-91-7415-686-7 (ISBN)
Presentation
2010-06-11, E2, Lindstedtsvägen 3, KTH, Stockholm, 10:00 (English)
Opponent
Supervisors
Available from: 2010-05-18 Created: 2010-05-18 Last updated: 2010-05-19Bibliographically approved

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