So-Kuen Chan. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1992. / Includes bibliographical references (leaves 99-102). / Chapter Chapter One --- Preview --- p.1 / Chapter Section 1 --- Introduction --- p.1 / Chapter Section 2 --- The Life Time Distribution --- p.4 / Chapter 2.1 --- Exponential Distribution --- p.5 / Chapter 2.2 --- Gamma Distribution --- p.6 / Chapter 2.3 --- Weibull Distribution --- p.7 / Chapter 2.4 --- Lognormal Distribution --- p.10 / Chapter Section 3 --- Nonparametric Inference for Geometric Process --- p.13 / Chapter 3.1 --- Test for Geometric Process --- p.13 / Chapter 3.2 --- Nonparametric Estimation Method --- p.17 / Chapter Section 4 --- Test for Distribution --- p.20 / Chapter 4.1 --- Graphical Method --- p.20 / Chapter 4.2 --- KS-test --- p.22 / Chapter 4.3 --- x2 GOF-test --- p.27 / Chapter 4.4 --- F-test (Exponential Dist.) --- p.28 / Chapter Chapter Two --- Parametric Inference for Geometric Process --- p.29 / Chapter Chapter Three --- Simulations --- p.39 / Chapter Chapter Four --- Examples --- p.49 / Chapter Chapter Five --- Comparison and Conclusion --- p.57 / Tables and Graphs --- p.61 / References --- p.99

by Tung-lok Ng. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1990. / Bibliography: leaves 57-59. / Chapter Chapter 1 --- Introduction --- p.1 / Chapter Chapter 2 --- Full Maximum Likelihood Estimation of the General Model --- p.4 / Chapter 2.1 --- Introduction --- p.4 / Chapter 2.2 --- Model --- p.4 / Chapter 2.3 --- Identification of the model --- p.5 / Chapter 2.4 --- Maximum likelihood estimation --- p.7 / Chapter 2.5 --- Computational Procedure --- p.12 / Chapter 2.6 --- Tests of Hypothesis --- p.13 / Chapter 2.7 --- Example --- p.14 / Chapter Chapter 3 --- Bayesian Analysis of Stochastic Prior Information --- p.17 / Chapter 3.1 --- Introduction --- p.17 / Chapter 3.2 --- Bayesian Analysis of the general model --- p.18 / Chapter 3.3 --- Computational Procedure --- p.22 / Chapter 3.4 --- Test the Compatibility of the Prior Information --- p.24 / Chapter 3.5 --- Example --- p.25 / Chapter Chapter 4 --- Simulation Study --- p.27 / Chapter 4.1 --- Introduction --- p.27 / Chapter 4.2 --- Simulation1 --- p.27 / Chapter 4.3 --- Simulation2 --- p.30 / Chapter 4.4 --- Summary and Discussion --- p.31 / Chapter Chapter 5 --- Concluding Remarks --- p.33 / Tables / References --- p.57

Thesis (Ph.D.)--Boston University / PLEASE NOTE: Boston University Libraries did not receive an Authorization To Manage form for this thesis or dissertation. It is therefore not openly accessible, though it may be available by request. If you are the author or principal advisor of this work and would like to request open access for it, please contact us at open-help@bu.edu. Thank you. / This dissertation is dedicated to optimization of Stochastic Hybrid Systems (SHS). The concentration is on both online optimization of these systems and extending the known optimal policies in Discrete-Event Systems (DES) to a broader context of SHS. A SHS involves both continuous and discrete dynamics and is suitable for modeling almost any physical system of interest. The first part of this dissertation focuses on applications of SHS and, particularly, a subclass known as Stochastic Flow Models (SFM) used in fluid scheduling. To this end, a classic problem for optimally allocating a resource to multiple competing user queues is considered in the DES context and placed in the framework of SFMs. Infinitesimal Perturbation Analysis (IPA) is used to calculate the gradient estimates for the average holding cost of this system with respect to resource allocation parameters. The monotonicity property of these estimates allows us to prove the optimality of a well-known rule called the "c - mu-rule" under non-idling policies. Furthermore, nonlinear cost functions are considered, yielding simple distribution-free cost sensitivity estimates. Next, we take the first step in using IPA for optimally calculating timeout thresholds in SHS. A Transmission Control Protocol (TCP) communication link is used to examine the effectiveness of SHS and IPA in calculating derivative estimates of a goodput objective with respect to a timeout parameter. The analysis is also extended to the case of multinode communications. Our results reveal a great potential in using IPA to control delay thresholds and motivate more investigations in future. Finally, we propose a general framework for analysis and on-line optimization of SHS which facilitates the use of IPA. In doing so, we modify the previous structure of a Stochastic Hybrid Automaton (SHA) and show that every transition is associated with an explicit event which is defined through a "guard function." This enables us to uniformly treat all events observed on the sample path of the SHS. As a result, a unifying matrix notation for IPA equations is developed which eliminates the need for the case-by-case analysis of event classes as usually done in prior works involving IPA for SHS. / 2031-01-01

The thesis is devoted to non-stationary point process models as generalizations of the standard homogeneous Poisson process. The work can be divided in two parts. In the first part, we introduce a fractional non-homogeneous Poisson process (FNPP) by applying a random time change to the standard Poisson process. We characterize the FNPP by deriving its non-local governing equation. We further compute moments and covariance of the process and discuss the distribution of the arrival times. Moreover, we give both finite-dimensional and functional limit theorems for the FNPP and the corresponding fractional non-homogeneous compound Poisson process. The limit theorems are derived by using martingale methods, regular variation properties and Anscombe's theorem. Eventually, some of the limit results are verified via a Monte-Carlo simulation. In the second part, we analyze statistical point process models for durations between trades recorded in financial high-frequency trading data. We consider parameter settings for models which are non-stationary or very close to non-stationarity which is quite typical for estimated parameter sets of models fitted to financial data. Simulation, parameter estimation and in particular model selection are discussed for the following three models: a non-homogeneous normal compound Poisson process, the exponential autoregressive conditional duration model (ACD) and a Hawkes process model. In a Monte-Carlo simulation, we test the performance of the following information criteria for model selection: Akaike's information criterion, the Bayesian information criterion and the Hannan-Quinn information criterion. We are particularly interested in the relation between the rate of correct model selection and the underlying sample size. Our numerical results show that the model selection for the compound Poisson type model works best for small parameter numbers. Moreover, the results for Hawkes processes confirm the theoretical asymptotic distributions of model selection whereas for the ACD model the model selection exhibits adverse behavior in certain cases.

by Wong Yin Bun, Terence. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1998. / Includes bibliographical references (leaves 99-104). / Abstract also in Chinese. / List of Figures --- p.ix / List of Tables --- p.xi / Chapter I --- Preliminary --- p.1 / Chapter 1 --- Introduction --- p.2 / Chapter 1.1 --- Thesis themes --- p.4 / Chapter 1.1.1 --- Dynamical view of landscape --- p.4 / Chapter 1.1.2 --- Bottom-up self-feedback algorithm with memory --- p.4 / Chapter 1.1.3 --- Cooperation and competition --- p.5 / Chapter 1.1.4 --- Contributions to genetic algorithms --- p.5 / Chapter 1.2 --- Thesis outline --- p.5 / Chapter 1.3 --- Contribution at a glance --- p.6 / Chapter 1.3.1 --- Problem --- p.6 / Chapter 1.3.2 --- Approach --- p.7 / Chapter 1.3.3 --- Contributions --- p.7 / Chapter 2 --- Background --- p.8 / Chapter 2.1 --- Iterative stochastic searching algorithms --- p.8 / Chapter 2.1.1 --- The algorithm --- p.8 / Chapter 2.1.2 --- Stochasticity --- p.10 / Chapter 2.2 --- Fitness landscapes and its relation to neighborhood --- p.12 / Chapter 2.2.1 --- Direct searching --- p.12 / Chapter 2.2.2 --- Exploration and exploitation --- p.12 / Chapter 2.2.3 --- Fitness landscapes --- p.13 / Chapter 2.2.4 --- Neighborhood --- p.16 / Chapter 2.3 --- Species formation methods --- p.17 / Chapter 2.3.1 --- Crowding methods --- p.17 / Chapter 2.3.2 --- Deterministic crowding --- p.18 / Chapter 2.3.3 --- Sharing method --- p.18 / Chapter 2.3.4 --- Dynamic niching --- p.19 / Chapter 2.4 --- Summary --- p.21 / Chapter II --- Probabilistic Binary Hierarchical Search --- p.22 / Chapter 3 --- The basic algorithm --- p.23 / Chapter 3.1 --- Introduction --- p.23 / Chapter 3.2 --- Search space reduction with binary hierarchy --- p.25 / Chapter 3.3 --- Search space modeling --- p.26 / Chapter 3.4 --- The information processing cycle --- p.29 / Chapter 3.4.1 --- Local searching agents --- p.29 / Chapter 3.4.2 --- Global environment --- p.30 / Chapter 3.4.3 --- Cooperative refinement and feedback --- p.33 / Chapter 3.5 --- Enhancement features --- p.34 / Chapter 3.5.1 --- Fitness scaling --- p.34 / Chapter 3.5.2 --- Elitism --- p.35 / Chapter 3.6 --- Illustration of the algorithm behavior --- p.36 / Chapter 3.6.1 --- Test problem --- p.36 / Chapter 3.6.2 --- Performance study --- p.38 / Chapter 3.6.3 --- Benchmark tests --- p.45 / Chapter 3.7 --- Discussion and analysis --- p.45 / Chapter 3.7.1 --- Hierarchy of partitions --- p.45 / Chapter 3.7.2 --- Availability of global information --- p.47 / Chapter 3.7.3 --- Adaptation --- p.47 / Chapter 3.8 --- Summary --- p.48 / Chapter III --- Cooperation and Competition --- p.50 / Chapter 4 --- High-dimensionality --- p.51 / Chapter 4.1 --- Introduction --- p.51 / Chapter 4.1.1 --- The challenge of high-dimensionality --- p.51 / Chapter 4.1.2 --- Cooperation - A solution to high-dimensionality --- p.52 / Chapter 4.2 --- Probabilistic Cooperative Binary Hierarchical Search --- p.52 / Chapter 4.2.1 --- Decoupling --- p.52 / Chapter 4.2.2 --- Cooperative fitness --- p.53 / Chapter 4.2.3 --- The cooperative model --- p.54 / Chapter 4.3 --- Empirical performance study --- p.56 / Chapter 4.3.1 --- pBHS versus pcBHS --- p.56 / Chapter 4.3.2 --- Scaling behavior of pcBHS --- p.60 / Chapter 4.3.3 --- Benchmark test --- p.62 / Chapter 4.4 --- Summary --- p.63 / Chapter 5 --- Deception --- p.65 / Chapter 5.1 --- Introduction --- p.65 / Chapter 5.1.1 --- The challenge of deceptiveness --- p.65 / Chapter 5.1.2 --- Competition: A solution to deception --- p.67 / Chapter 5.2 --- Probabilistic cooperative-competitive binary hierarchical search --- p.67 / Chapter 5.2.1 --- Overview --- p.68 / Chapter 5.2.2 --- The cooperative-competitive model --- p.68 / Chapter 5.3 --- Empirical performance study --- p.70 / Chapter 5.3.1 --- Goldberg's deceptive function --- p.70 / Chapter 5.3.2 --- "Shekel family - S5, S7, and S10" --- p.73 / Chapter 5.4 --- Summary --- p.74 / Chapter IV --- Finale --- p.78 / Chapter 6 --- A new genetic operator --- p.79 / Chapter 6.1 --- Introduction --- p.79 / Chapter 6.2 --- Variants of the integration --- p.80 / Chapter 6.2.1 --- Fixed-fraction-of-all --- p.83 / Chapter 6.2.2 --- Fixed-fraction-of-best --- p.83 / Chapter 6.2.3 --- Best-from-both --- p.84 / Chapter 6.3 --- Empricial performance study --- p.84 / Chapter 6.4 --- Summary --- p.88 / Chapter 7 --- Conclusion and Future work --- p.89 / Chapter A --- The pBHS Algorithm --- p.91 / Chapter A.1 --- Overview --- p.91 / Chapter A.2 --- Details --- p.91 / Chapter B --- Test problems --- p.96 / Bibliography --- p.99

Faculty of Science, School of Statistics & Actuarial Science, MSC Dissertation / This thesis follows a direction of research that deals with the theoretical foundations of stochastic differential equations on manifolds and a geometric analysis of the fundamental equations in nonlinear filtering theory. We examine the importance of modern differential geometry in developing an invariant theory of stochastic processes on manifolds, which allow us to extend current filtering techniques to an important class of manifolds. Furthermore, these tools provide us with greater insight to the infinite-dimensional nonlinear filtering problem. In particular, we apply our geometric analysis to the so called unnormalized conditional density approach expounded by M. Zakai. We exploit the geometric setting to study the geometric and algebraic properties of the Zakai equation, which is a linear stochastic partial differential equation. In particular, we investigate the use of Lie algebras and group invariance techniques for dimension analysis and for the reduction of the Zakai equation. Finally, we utilize simulation to demonstrate the superiority of the Zakai equation over the extended Kalman filter for a passive radar tracking problem.

Let P(ε) = P0 + A(ε) be a stochasticity preserving analytic perturbation of a stochastic matrix P0. We characterize the hybrid Cesaro limit lim 1 N(ε) Pk(ε), ε↓0 N(ε) ∑ where N(ε) ↑ ∞ as ε ↓ 0, when P0 has eigenvalues on the unit circle in the complex plane other than 1.

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Multistage stochastic programming is an important tool in medium to long term planning where there are uncertainties in the data. In this thesis, we consider a special case of multistage stochastic programming in which each subprogram is a convex quadratic program. The results are also applicable if the quadratic objectives are replaced by convex piecewise quadratic functions. Convex piecewise quadratic functions have important application in financial planning problems as they can be used as very flexible risk measures. The stochastic programming problems can be used as multi-period portfolio planning problems tailored to the need of individual investors. Using techniques from convex analysis and sensitivity analysis, we show that each subproblem of a multistage quadratic stochastic program is a polyhedral piecewise quadratic program with convex Lipschitz objective. The objective of any subproblem is differentiable with Lipschitz gradient if all its descendent problems have unique dual variables, which can be guaranteed if the linear independence constraint qualification is satisfied. Expression for arbitrary elements of the subdifferential and generalized Hessian at a point can be calculated for quadratic pieces that are active at the point. Generalized Newton methods with linesearch are proposed for solving multistage quadratic stochastic programs. The algorithms converge globally. If the piecewise quadratic objective is differentiable and strictly convex at the solution, then convergence is also finite. A generalized Newton algorithm is implemented in Matlab. Numerical experiments have been carried out to demonstrate its effectiveness. The algorithm is tested on random data with 3, 4 and 5 stages with a maximum of 315 scenarios. The algorithm has also been successfully applied to two sets of test data from a capacity expansion problem and a portfolio management problem. Various strategies have been implemented to improve the efficiency of the proposed algorithm. We experimented with trust region methods with different parameters, using an advanced solution from a smaller version of the original problem and sorting the stochastic right hand sides to encourage faster convergence. The numerical results show that the proposed generalized Newton method is a highly accurate and effective method for multistage quadratic stochastic programs. For problems with the same number of stages, solution times increase linearly with the number of scenarios.