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Contributions to the Theory of Monte Carlo and Quasi-Monte Carlo Methods by Giray Okten (Paperback, 1999)

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Quasi-Monte Carlo methods, which are often described as deterministic versions of Monte Carlo methods, were introduced in the 1950s by number theoreticians. They improve several deficiencies of Monte Carlo methods; such as providing estimates with deterministic bounds and avoiding the paradoxical difficulty of generating random numbers in a computer. However, they have their own drawbacks. First, although they provide faster convergence than Monte Carlo methods asymptotically, the advantage may not be practical to obtain in high dimensional problems. Second, there is not a practical way to measure the error of a quasi-Monte Carlo simulation. Finally, unlike Monte Carlo methods, there is a scarcity of error reduction techniques for these methods. In this dissertation, we attempt to provide remedies for the disadvantages of quasi-Monte Carlo methods mentioned above. In the first part of the dissertation, a hybrid-Monte Carlo sequence designed to obtain error reduction in high dimensions is studied. Probabilistic results on the discrepancy of this sequence as well as results obtained by applying the sequence to problems from numerical integration and mathematical finance are presented. In the second part of the dissertation, a new hybrid-Monte Carlo method is introduced, in an attempt to obtain a practical statistical error analysis using low-discrepancy sequences. It is applied to problems from mathematical finance and particle transport theory to compare its effectiveness with the conventional methods. In the last part of the dissertation, a generalized quasi-Monte Carlo integration rule is introduced. A Koksma-Hlawka type inequality for the rule is proved, using a new concept for the variation of a function. As a consequence of the rule, error reduction techniques and in particular an importance sampling type statement are derived. Problems from different disciplines are used as practical tests for our methods. The numerical results obtained in favor of the methods suggest the practical advantages that can be realized by their use in a wide variety of applications.

Product Identifiers

Publisher
Dissertation.Com
ISBN-13
9781581120417
eBay Product ID (ePID)
103717078

Product Key Features

Author
Giray Okten
Publication Name
Contributions to the Theory of Monte Carlo and Quasi-Monte Carlo Methods
Format
Paperback
Language
English
Subject
Mathematics
Publication Year
1999
Type
Textbook
Number of Pages
108 Pages

Dimensions

Item Height
216mm
Item Width
140mm
Item Weight
145g

Additional Product Features

Title_Author
Giray Okten

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Contributions to the Theory of Monte Carlo and Quasi-Monte Carlo Methods by Giray Okten (Paperback, 1999)

About this product

Product Information

Product Identifiers

Product Key Features

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Additional Product Features

Best Selling in Textbooks

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