Computational aspects of the numerical solution of SDEs

In the last 30 to 40 years, many researchers have combined to build the knowledge base of theory and solution techniques that can be applied to the case of differential equations which include the effects of noise. This class of ``noisy'' differential equations is now known as stochastic differential equations (SDEs). Markov diffusion processes are included within the field of SDEs through the drift and diffusion components of the Itô form of an SDE. When these drift and diffusion components are moderately smooth functions, then the processes' transition probability densities satisfy the Fokker-Planck-Kolmogorov (FPK) equation -- an ordinary partial differential equation (PDE). Thus there is a mathematical inter-relationship that allows solutions of SDEs to be determined from the solution of a noise free differential equation which has been extensively studied since the 1920s. The main numerical solution technique employed to solve the FPK equation is the classical Finite Element Method (FEM). The FEM is of particular importance to engineers when used to solve FPK systems that describe noisy oscillators. The FEM is a powerful tool but is limited in that it is cumbersome when applied to multidimensional systems and can lead to large and complex matrix systems with their inherent solution and storage problems. I show in this thesis that the stochastic Taylor series (TS) based time discretisation approach to the solution of SDEs is an efficient and accurate technique that provides transition and steady state solutions to the associated FPK equation. The TS approach to the solution of SDEs has certain advantages over the classical techniques. These advantages include their ability to effectively tackle stiff systems, their simplicity of derivation and their ease of implementation and re-use. Unlike the FEM approach, which is difficult to apply in even only two dimensions, the simplicity of the TS approach is independant of the dimension of the system under investigation. Their main disadvantage, that of requiring a large number of simulations and the associated CPU requirements, is countered by their underlying structure which makes them perfectly suited for use on the now prevalent parallel or distributed processing systems. In summary, l will compare the TS solution of SDEs to the solution of the associated FPK equations using the classical FEM technique. One, two and three dimensional FPK systems that describe noisy oscillators have been chosen for the analysis. As higher dimensional FPK systems are rarely mentioned in the literature, the TS approach will be extended to essentially infinite dimensional systems through the solution of stochastic PDEs. In making these comparisons, the advantages of modern computing tools such as computer algebra systems and simulation software, when used as an adjunct to the solution of SDEs or their associated FPK equations, are demonstrated.

Customer repurchase intention: a general structural equation model

This paper develops a general service sector model of repurchase intention from the consumer theory literature. A key contribution of the structural equation model is the incorporation of customer perceptions of equity and value and customer brand preference into an integrated repurchase intention analysis. The model describes the extent to which customer repurchase intention is influenced by seven important factors – service quality, equity and value, customer satisfaction, past loyalty, expected switching cost and brand preference. The general model is applied to customers of comprehensive car insurance and personal superannuation services. The analysis finds that although perceived quality does not directly affect customer satisfaction, it does so indirectly via customer equity and value perceptions. The study also finds that past purchase loyalty is not directly related to customer satisfaction or current brand preference and that brand preference is an intervening factor between customer satisfaction and repurchase intention. The main factor influencing brand preference was perceived value with customer satisfaction and expected switching cost having less influence.

Shear- free perfect fluids with solenoidal magnetic curvature and a γ-law equation of state

We show that shear-free perfect fluids obeying an equation of state p = (γ − 1)μ are non-rotating or non-expanding under the assumption that the spatial divergence of the magnetic part of the Weyl tensor is zero.

Interpreting Fanger's comfort equation within the adaptive paradigm

This paper reviews the evolution of Fanger's heat balance equation in regard of adaptive opportunities. Heat balance and adaptive response are integrated into one model as two fundamental aspects of human-environment interaction that define thermal comfort perception, rather than being seen as two concepts of alternative comfort paradigms. The paper suggests to extent Fanger's model with a heat storage term in order to account for comfort perception under transient thermal conditions, and to review Fanger's modelling assumptions in order to allow for a greater variety of adaptive response options. In the presented model heat exchange is modulated through adaptation of physiological, environmental and behavioural parameters in the human-environment system defined through Fanger's heat exchange equations. A computational prototype is implemented to determine 'comfortable' values and ranges of the six comfort dimensions alternatively to Fanger's comfort indices. Thereby values of for example 'comfortable' clothing and metabolic rate are results rather than necessary input parameters, which are difficult to determine. This approach allows generating design advice for physical, organisational and social environments based on heat balance calculation in the six-dimensional opportunity space defined through Fanger's comfort equation. A starting point for the development of a dynamic adaptive comfort model is set.

Structural equation modelling of complex sample survey : an application to brand signalling data

The purpose of this paper is to present an empirical analysis of complex sample data with regard to the biasing effect of nonindependence of observations on standard error parameter estimates. In a two-factor confirmatory factor analysis model, using real data, we show how the bias in standard errors can be derived when the nonindependence is ignored. We demonstrate that the standard error bias produced by the nonindependence of observations can be considerable and we briefly discuss solutions to overcome the problem.

Structural equation modelling : tips for getting started with your research

At a time when numerical expression of data is becoming more important in the business of obtaining grant money research tools such as structural equation modelling (SEM) are becoming more popular. Structural equation modelling enables researchers to show relationships between variables numerically. It is of particular use to educational researchers who are interested in developing or using standard questionnaires in their research. This session will introduce SEM and explore its uses in educational research to enable the reader to decide whether it is a tool to use to add an extra dimension to their research findings.

Economic accountability in the context of local governance in the Philippines : a structural equation modelling approach

This study posits that by virtue of the enabling role of local governments, the economic development of their locality must be at the core of their public accountability, which is referred to here as “economic accountability”. Grounded on this idea of accountability, along with enabling theory and institutional theory, the study presents empirical evidence supportive of the argument that the enabling role of local governments, as manifested in a capacity to establish or adhere to formal institutional arrangements, has a direct impact on the entrepreneurial strategic posture and performance of local small and medium enterprises (SMEs) which are key players in local economic development.The results of the structural equation modelling support the view that institutional arrangements as manifestations of the enabling role of city governments are positively associated with an entrepreneurial strategic posture of local firms, which consequently improves the firms’ overall economic performance. Therefore, SME development in particular, and local economic development in general, should be part of the economic accountability of local governments in the Philippine context of local governance.