published_or_final_version / Mathematics / Master / Master of Philosophy

published_or_final_version / Statistics and Actuarial Science / Doctoral / Doctor of Philosophy

No description available.

In this thesis, a wavelet-based prediction method is developed for concealing packet-loss effects in wireless channels. The proposed method utilizes a wavelet decomposition algorithm in order to process the data and then applies the well known linear prediction technique to estimate one or more approximation coefficients as necessary at the lowest resolution level. The predicted sample stream is produced by using the predicted approximation coefficients and by exploiting certain sample value patterns in the detail coefficients. In order to test the effectiveness of the proposed scheme, a wireless channel based on a three-state Markov model is developed and simulated. Simulation results for transmission of image and speech packet streams over a wireless channel are reported for both the wavelet-based prediction and direct linear prediction. In all the simulations run in this work, the wavelet-based method outperformed the direct linear prediction method. / Hellenic Navy author.

A thesis submitted for the degree of Doctor of Philosophy 2013 / This thesis presents a range of related pricing kernel models that are driven by incomplete information about a series of future unknowns. These unknowns may, for instance, represent fundamental macroeconomic, political or social random variables that are revealed at future times. They may also represent latent or hidden factors that are revealed asymptotically. We adopt the information-based approach of Brody, Hughston and Macrina (BHM) to model the information processes associated with the random variables. The market filtration is generated collectively by these information processes. By directly modelling the pricing kernel, we generate information-sensitive arbitrage-free models for the term structure of interest rates, the excess rate of return required by investors, and security prices. The pricing kernel is modelled by a supermartingale to ensure that nominal interest rates remain non-negative. To begin with, we primarily investigate finite-time pricing kernel models that are sensitive to Brownian bridge information. The BHM framework for the pricing of credit-risky instruments is extended to a stochastic interest rate setting. In addition, we construct recovery models, which take into consideration information about, for example, the state of the economy at the time of default. We examine various explicit examples of analytically tractable information-driven pricing kernel models. We develop a model that shares many of the features of the rational lognormal model, and investigate examples of heat kernel models. It is shown that these models may result in discount bonds and interest rates being bounded by deterministic functions. In certain situations, incoming information about random variables may exhibit jumps. To this end, we construct a more general class of nite-time pricing kernel models that are driven by Levy random bridges. Finally, we model the aggregate impact of uncertainties on a nancial market by randomised mixtures of Levy and Markov processes respectively. It is assumed that market participants have incomplete information about the underlying random mixture. We apply results from non-linear ltering theory and construct Flesaker-Hughston models and in nite-time heat kernel models based on these randomised mixtures.

A dissertation submitted to the Faculty of Science, University of the Witwatersrand, in fulfillment of the requirements for the degree of Doctor of Philosophy, April 2013. / In a series of papers by Wen-Chi Kuo, Coenraad Labuschagne and Bruce Watson results of martingale theory were generalised to the abstract setting of Riesz spaces. This thesis presents a survey of those results proved and aims to expand upon the work of these authors. In particular, independence results will be considered and these will be used to generalise well known results in the theory of Markov processes to Riesz spaces. Mixingales and quasi-martingales will be translated to the Riesz space setting.

Thesis (M.Sc.)--University of the Witwatersrand, Faculty of Science, School of Computer Science and Applied Mathematics, 2017. / Partially Observable Markov Decision Processes (POMDPs) provide a principled mathematical framework allowing a robot to reason about the consequences of actions and observations with respect to the agent's limited perception of its environment. They allow an agent to plan and act optimally in uncertain environments. Although they have been successfully applied to various robotic tasks, they are infamous for their high computational cost. This thesis demonstrates the use of knowledge transfer, learned from previous experiences, to accelerate the learning of POMDP tasks. We propose that in order for an agent to learn to solve these tasks quicker, it must be able to generalise from past behaviours and transfer knowledge, learned from solving multiple tasks, between di erent circumstances. We present a method for accelerating this learning process by learning the statistics of action choices over the lifetime of an agent, known as action priors. Action priors specify the usefulness of actions in situations and allow us to bias exploration, which in turn improves the performance of the learning process. Using navigation domains, we study the degree to which transferring knowledge between tasks in this way results in a considerable speed up in solution times. This thesis therefore makes the following contributions. We provide an algorithm for learning action priors from a set of approximately optimal value functions and two approaches with which a prior knowledge over actions can be used in a POMDP context. As such, we show that considerable gains in speed can be achieved in learning subsequent tasks using prior knowledge rather than learning from scratch. Learning with action priors can particularly be useful in reducing the cost of exploration in the early stages of the learning process as the priors can act as mechanism that allows the agent to select more useful actions given particular circumstances. Thus, we demonstrate how the initial losses associated with unguided exploration can be alleviated through the use of action priors which allow for safer exploration. Additionally, we illustrate that action priors can also improve the computation speeds of learning feasible policies in a shorter period of time. / MT2018

by Shing-chiang Wong. / Bibliography: leaf 73 / Thesis (M.Ph.)--Chinese University of Hong Kong, 1986

Ng Hon Keung Tony. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (leaves 85-87). / Abstracts in English and Chinese. / Chapter Chapter 1 --- Introduction --- p.1 / Chapter Chapter 2 --- Probability Analysis of Consecutive-k-out-of-n: F system with (k-l)-step Markov Dependence --- p.11 / Chapter 2.1 --- Model and Assumptions --- p.11 / Chapter 2.2 --- Find Out the Failure Risk of the System --- p.17 / Chapter 2.3 --- The Linear Consecutive-3-out-of-4: F Repairable system with 2-step Markov Dependence --- p.27 / Chapter 2.3.1 --- Failure risk of the system --- p.27 / Chapter 2.3.2 --- Priority repair rule --- p.32 / Chapter 2.4 --- The Circular Consecutive-3-out-of-4: F Repairable system with 2-step Markov Dependence --- p.41 / Chapter 2.4.1 --- Failure risk of the system --- p.41 / Chapter 2.4.2 --- Priority repair rule --- p.47 / Chapter Chapter 3 --- System Analysis for Linear Consecutive-3-out-of-4: F system with 2-step Markov Dependence by Laplace Transform Method --- p.57 / Chapter Chapter 4 --- Reliability Indices for Consecutive-3-out-of-4: F system with 2-step Markov Dependence by Numerical Method and Simulation Study --- p.69 / Chapter 4.1 --- Numerical Method --- p.69 / Chapter 4.1.1 --- Linear consecutive-3-out-of-4: F repairable system with 2-step Markov dependence --- p.70 / Chapter 4.1.2 --- Comparison between Laplace transform method and numerical method --- p.72 / Chapter 4.1.3 --- Circular consecutive-3-out-of-4: F repairable system with 2-step Markov dependence --- p.75 / Chapter 4.2 --- Numerical Results --- p.75 / Chapter 4.3 --- Simulation Study --- p.78 / Chapter 4.4 --- Comparison between Simulation Method and Numerical Method --- p.79 / FIGURES 1 to 7 --- p.82-84 / REFERENCES --- p.85-87

by Chi-Wai Lee. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (leaves 112-117). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgement --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Background and Motivations --- p.1 / Chapter 1.2 --- Problem Definition --- p.5 / Chapter 1.3 --- Contributions --- p.5 / Chapter 1.4 --- Thesis Organization --- p.7 / Chapter 2 --- Literature Review --- p.8 / Chapter 2.1 --- Electronic Commerce --- p.8 / Chapter 2.2 --- Agents for Electronic Commerce --- p.9 / Chapter 2.3 --- Online Auctions --- p.11 / Chapter 2.3.1 --- Business Models --- p.12 / Chapter 2.3.2 --- Auction Formats --- p.13 / Chapter 2.3.3 --- Time Duration of Auctions --- p.14 / Chapter 2.3.4 --- Minimum Bids and Reserve Prices --- p.15 / Chapter 2.3.5 --- Auction Properties and Bidder Behaviours --- p.15 / Chapter 2.3.6 --- "Comparison of English, Dutch and Double auction" --- p.16 / Chapter 2.4 --- Agents Developing Tools and Tool-kits --- p.17 / Chapter 2.5 --- Limitations of Agent Tool-kits --- p.18 / Chapter 2.6 --- Markov Processes for Stochastic Modeling --- p.20 / Chapter 2.6.1 --- Continuous Time Markov Chain --- p.21 / Chapter 2.6.2 --- Poisson Arrival Model --- p.22 / Chapter 2.6.3 --- Example: discrete time Markov chain with stationary probabilities --- p.22 / Chapter 3 --- Markov Chain Model --- p.25 / Chapter 3.1 --- Markov Chain for English Auction --- p.25 / Chapter 3.1.1 --- Variables --- p.27 / Chapter 3.1.2 --- Auction Assumptions --- p.27 / Chapter 3.1.3 --- Bidder Assumptions --- p.29 / Chapter 3.1.4 --- Propositions of the Markov Model --- p.31 / Chapter 3.1.5 --- Tractability --- p.35 / Chapter 3.2 --- Markov Chain for Dutch Auction --- p.38 / Chapter 3.2.1 --- Variables --- p.39 / Chapter 3.2.2 --- Model Assumptions --- p.39 / Chapter 3.2.3 --- Propositions of the Markov Model --- p.42 / Chapter 3.2.4 --- Tractability --- p.43 / Chapter 3.3 --- Progression of the Price Vector for English and Dutch Auction --- p.43 / Chapter 3.4 --- Markov Chain for Double auction --- p.45 / Chapter 3.4.1 --- Variables --- p.47 / Chapter 3.4.2 --- Model Assumptions --- p.47 / Chapter 3.4.3 --- Propositions of the Markov Model --- p.49 / Chapter 3.4.4 --- Tractability --- p.53 / Chapter 3.5 --- Progression of the Price Vector for Double Auction --- p.53 / Chapter 3.6 --- Summary --- p.54 / Chapter 4 --- System Design --- p.57 / Chapter 4.1 --- System Features --- p.58 / Chapter 4.2 --- System Architecture --- p.59 / Chapter 4.2.1 --- System Workflow --- p.60 / Chapter 4.2.2 --- Communication Layer --- p.61 / Chapter 4.2.3 --- Agent Logic Layer --- p.62 / Chapter 4.2.4 --- Database Abstraction Layer --- p.62 / Chapter 4.3 --- Roles of the Agents --- p.62 / Chapter 4.4 --- Implementation Details --- p.65 / Chapter 4.4.1 --- Choosing a Scripting Language --- p.65 / Chapter 4.4.2 --- Choosing a Database --- p.68 / Chapter 4.4.3 --- Server-Side Java with Jakarta-tomcat --- p.69 / Chapter 4.4.4 --- Agent API --- p.70 / Chapter 4.4.5 --- Class java.agent.Agent --- p.72 / Chapter 4.5 --- Summary --- p.73 / Chapter 5 --- Experimental Results --- p.75 / Chapter 5.1 --- Simulation Environment --- p.75 / Chapter 5.2 --- Experiment One: A small English auction --- p.76 / Chapter 5.3 --- Experiment Two: A large English auction --- p.80 / Chapter 5.4 --- Experiment Three: A small Dutch auction --- p.82 / Chapter 5.5 --- Experiment Four: A large Dutch auction --- p.83 / Chapter 5.6 --- Experiment Five: Partial knowledge on other BAs --- p.84 / Chapter 5.7 --- Experiment Six: Partial knowledge on closing time --- p.86 / Chapter 5.8 --- Experiment Seven: A small Double auction --- p.87 / Chapter 5.9 --- Comparisons and Discussions --- p.89 / Chapter 5.10 --- Summary --- p.90 / Chapter 6 --- Conclusion --- p.91 / Chapter A --- Markov Chain for English Auction --- p.93 / Chapter A.1 --- Graphs of F and F* Functions --- p.93 / Chapter A.2 --- Solution of a Small Example --- p.96 / Chapter A.2.1 --- Computation of Transition Probabilities --- p.97 / Chapter A.2.2 --- Progression of the Price Vector --- p.97 / Chapter B --- Markov Chain for Double Auction --- p.101 / Chapter B.1 --- Graphs of Fb(vbi) and Fs(vsi) Functions --- p.101 / Chapter B.2 --- Solution of a Small Example --- p.102 / Chapter B.2.1 --- Computation of Transition Probabilities --- p.102 / Chapter C --- Implementation Details --- p.105 / Chapter C.1 --- Tables Design in MySQL --- p.105 / Chapter C.2 --- Sample Apache Configuration File --- p.109 / Bibliography --- p.112