In this thesis, we study the estimation of the nonlinear conditionalrisk-neutral density function (RND) in discrete time. Specifically, weevaluate the extent to which the estimated nonlinear conditional RNDvaluable insights to answer relevant economic questions regarding to optionpricing, the measurement of invertors' preferences and portfolio choice.We make use of large dataset of options contracts written on the S&P 500index from 1996 to 2011, to estimate the parameters of the conditional RNDfunctions by minimizing the squared option pricing errors delivered by thenonlinear models studied in the thesis.In the first essay, we show that a semi-nonparametric option pricing modelwith GARCH variance outperforms several benchmarks models in-sample andout-of-sample. In the second essay, we show that a simple two-state regimeswitching model in volatility is not able to fully account for the pricingkernel and the risk aversion puzzle; however, it provides a reasonablecharacterisation of the time-series properties of the estimated riskaversion.In the third essay, we evaluate linear stochastic discount factormodels using an out-of-sample financial metric. We find that multifactormodels outperform the CAPM when this metric is used, and that modelsproducing the best fit in-sample are also those exhibiting the bestperformance out-of-sample.

Researchers have shown that by combining multiple input multiple output (MIMO) techniques with CDMA then higher gains in capacity, reliability and data transmission speed can be attained. But a major drawback of MIMO-CDMA systems is multiple access interference (MAI) which can reduce the capacity and increase the bit error rate (BER), so statistical analysis of MAI becomes a very important factor in the performance analysis of these systems. In this thesis, a detailed analysis of MAI is performed for binary phase-shift keying (BPSK) signals with random signature sequence in Raleigh fading environment and closed from expressions for the probability density function of MAI and MAI with noise are derived. Further, probability of error is derived for the maximum Likelihood receiver. These derivations are verified through simulations and are found to reinforce the theoretical results. Since the performance of MIMO suffers significantly from MAI and inter-symbol interference (ISI), equalization is needed to mitigate these effects. It is well known from the theory of constrained optimization that the learning speed of any adaptive filtering algorithm can be increased by adding a constraint to it, as in the case of the normalized least mean squared (NLMS) algorithm. Thus, in this work both linear and non-linear decision feedback (DFE) equalizers for MIMO systems with least mean square (LMS) based constrained stochastic gradient algorithm have been designed. More specifically, an LMS algorithm has been developed , which was equipped with the knowledge of number of users, spreading sequence (SS) length, additive noise variance as well as MAI with noise (new constraint) and is named MIMO-CDMA MAI with noise constrained (MNCLMS) algorithm. Convergence and tracking analysis of the proposed algorithm are carried out in the scenario of interference and noise limited systems, and simulation results are presented to compare the performance of MIMO-CDMA MNCLMS algorithm with other adaptive algorithms.

In this work, we propose three control strategies from different perspectives to solve the alignment problem for different optical wireless communication (OWC) systems. • Experimental modeling based strategy: we model and analyze the vibration effects on the stationary OWC system (e.g. urban free-space optical (FSO) communication system in our case). The proposed Bifurcated-Gaussian (B-G) distribution model of the receiver optical power is derived under different vibra- tion levels and link distances using the nonlinear iteration method. Besides, the UFSO channel under the effects of both vibration and atmospheric turbulence is also explored under three atmospheric turbulence conditions. Our proposed B-G distribution model helps to easily evaluate the link performance of UFSO systems and paves the way for constructing completed auxiliary control subsys- tems for robust UFSO links. • Extremum seeking control based strategy: we propose an extremum seeking control (ESC) based strategy for the mobile OWC system. Our proposed ap- proach consists of coarse alignment and fine alignment. The coarse alignment using feedback proportional-derivative (PD) control is responsible for tracking and following the receiver. For fine alignment, the perturbation-based extremum seeking control (ESC) is adopted for a continuous search for the optimal posi- tion, where the received optical power is maximum in the presence of distur- bance. The proposed approach is simple, effective, and easy to implement. • Time scale theory based strategy: we design a time scale based Kalman filter for the intermittent OWC system. First, the algorithm of Kalman filter on time scales is presented, followed by several numerical examples for interpretation and analysis. The design of Kalman filter on time scales for our simulated vibrating OWC system is then discussed, whose results are analyzed thoroughly and further validated by a reference system. The proposed strategy has great potential for solving the problem of observer design in the case of intermittent received signals (non-uniform measurements) and paves the way for further controller design. The three proposed control strategies directly or indirectly solve the beam align- ment problem for optical communication systems, supporting the development of robust optical communication link.

<div>Computational studies are performed on a Cambridge Stratified Swirl burner (SwB), a lean premixed stratified flame, by using the Reynolds Averaged Navier Stokes (RANS) model and the transported Probability Density Function (PDF) model. The SwB burner was measured</div><div>by Sweeney et al. (Combustion and Flame, 2012, 159: 2896-2911), and comprehensive data are available for model validation, e.g., the mean and root-mean-square values of velocity, temperature, and species mass fractions. The experimental data are available for sixteen different cases to investigate flames in premixed and stratified regimes, with or without swirl. In this study, we consider only non-swirling, premixed and stratified cases. Different</div><div>turbulence models are examined in the modeling studies, and the Reynolds Stress model with standard model constant values is found to perform well with the transported PDF model. A joint PDF for enthalpy and species mass fractions allows for the highly non-linear reaction term in the transport equation to be completely closed. The mixing term arising from molecular diffusion is not closed and requires modeling which is a significant challenge. For the SwB, we consider a series of mixing models including the Interaction by Exchange with the Mean (IEM) mixing model with different mixing model constants, the Modified Curl model, and two mixing models designed for premixed combustion from the literature. We first examine the models in the non-stratified/premixed case (SwB1) to isolate the effect</div><div>of other conditions from stratification on the model predictions. The stratification is then added in two levels, a moderately stratified case (SwB5) and a highly stratified case (SwB9). The predicted results are compared with the experimental data at various locations, inside and outside the recirculation zone in the burner. In general, good agreement is obtained for the velocity fields inside the recirculation zone. Good agreement is also obtained</div><div>of the predicted and measured results is obtained for the mean values of temperature and species mass fractions. The scalar fluctuations are generally underpredicted. Overall, the employed modeling method is able to capture the mean flame structure reasonably well in lean premixed stratified flames. Some limitations are noticed, e.g., the underprediction of scalar fluctuations, and overprediction of CH4 concentration in the stratified cases. These observations are useful for guiding the future research directions.</div>

We describe basic notions of functional random elements and the space of functions L2 [0, 1]. We discuss the non-existence of a probability density functional and the re- quirements for integrating in a functional space. In Chapter 2, we define distribution functionals and introduce a goodness-of-fit test which utilises them. The concept of char- acteristic functionals follows in Chapter 3, along with the latest test for Gaussianity of functional random elements. We conclude the chapter with our own new goodness-of- fit test, where we prove the distribution of its test statistic under the alternative, then under the null hypothesis, and lastly the distribution of the bootstrapped test statistic. Finally, we illustrate the theory on a simulation study of the empirical significance level and power of the goodness-of-fit tests. 1

Subroutines are written to generate random numbers on the computer. Depending on the subroutine used, the generated random numbers follow the uniform, binomial, normal, chi-square, t, F, or gamma distribution. Each subroutine is tested using the chi-square goodness of fit test to verify that the random numbers generated by each subroutine follow the statistical distribution for which it is written. The interpretation of the test results indicates that each subroutine generates random numbers which closely approximates the theoretical distribution for which it is designed. The approach used in the subroutine which generates gamma distributed random numbers involves the use of numerical integration, whereas simpler techniques are used in all the other subroutines. Each subroutine is documented with a description of how to use it and an explanation of the methods used to obtain the random numbers which it is designed to generate. (77 pages)

The survival of our nation, during a nuclear exchange, depends upon an effective national defense structure. The prime weapon system in this defense structure is the ballistic missile. Although many factors enter into an evaluation of the effectiveness of a ballistic missile, one of the most important measure is accuracy. Without an accurate weapon system we have no weapon system. The Department of Defense has places emphasis on using a method of accuracy evaluation called "Probably Circular Error (CEP)." Probably Circular Error is defined as "The radius of a circle, centered at the intended target, within which 50% of the missiles would be expected to impact" or "The probability is 0.50 that an individual missile will impact within a circle whose radius is equal to the CEP." The statistical techniques and assumptions used in generation a CEP value will be investigated.

No description available.

No / This paper outlines the current challenges of driver behaviour modelling for real-world applications and presents the novel method to identify the pattern of usage to predict upcoming journeys in probability sense. The primary aim is to establish similarity between observed behaviour of drivers resulting in the ability to cluster them and deploy control strategies based on contextual intelligence and datadriven approach. The proposed approach uses the probability density function (PDF) driven by kernel density estimation (KDE) as a probabilistic approach to predict the type of the upcoming journey, expressed as duration and distance. Using the proposed method, the mathematical formulation and programming algorithm procedure have been indicated in detail, while the case study examples with the data visualisation are given for algorithm validation in simulation. / aiR-FORCE project, funded as Proof of Concept by the Institute of Digital Engineering

Yes / This paper presents a novel minimum entropy control algorithm for a class of stochastic nonlinear systems subjected to non-Gaussian noises. The entropy control can be considered as an optimization problem for the system randomness attenuation, but the mean value has to be considered separately. To overcome this disadvantage, a new representation of the system stochastic properties was given using the cumulant-generating function based on the moment-generating function, in which the mean value and the entropy was reflected by the shape of the cumulant-generating function. Based on the samples of the system output and control input, a time-variant linear model was identified, and the minimum entropy optimization was transformed to system stabilization. Then, an optimal control strategy was developed to achieve the randomness attenuation, and the boundedness of the controlled system output was analyzed. The effectiveness of the presented control algorithm was demonstrated by a numerical example. In this paper, a data-driven minimum entropy design is presented without pre-knowledge of the system model; entropy optimization is achieved by the system stabilization approach in which the stochastic distribution control and minimum entropy are unified using the same identified structure; and a potential framework is obtained since all the existing system stabilization methods can be adopted to achieve the minimum entropy objective.