51 
The Effects of Distortions on LinearSystem Identification and NonlinearCharacterisationWidanage, Widanalage Dhammika January 2008 (has links)
The thesis focuses on the identification of linear systems and those nonlinear systems which can be represented with purely linear dynamics and a zero memory nonlinearity in cascade. With the systems subjected to stationary Gaussian processes or periodic excitations and with or without external disturbances at the output, the linear dynamics are estimated as nonparametric or parametric models and any nonlinearity is characterised through the form of sign~ls appearing at its input and output. The main research of the first part of the thesis is concerned with nonparametric identification of linear systems with finite time stationary white Gaussian data, or finite gain and phase response measurements. The sources of errors leading to the uncertainty of the frequency response function of a system are identified and it is shown that there is a limit to the reduction in the variance when wind~wing the measured data and block overlap is employ~d. The direct use of expressions relating phase and gain responses lead to inaccurate results, and modifications to the functions and extrapolation methods are developed to give significant improvement in accuracy. The second part involves nonlinear system identification. By using a sinusoidal excitation, it is shown how the phase of a harmonic at the output relative to the input can be used to deduce the position of the nonlinearity in relation to the linear dynamics. Two procedures are developed to identify the dynamics and form of nonlinearity in the system. Further, it is shown how among a class of discrete time linear models, the autoregressive moving average with exogenous input (ARMAX) best describes the linear dynamics of a Hammerstein system while a BoxJenkins (BJ) best describes the linear dynamics of a Wiener system, in a mean square sense. The last part of the thesis gives a review for periodic perturbation signal design. Graphical user interfaces were developed to ease the generation of pseudo random and multilevel multiharmonic signals.

52 
Pricing discretely monitored barrier options and credit default swaps under Lévy processesde Innocentis, Marco January 2013 (has links)
We introduce a new, fast and accurate method to calculate prices and sensitivities of European vanilla and digital options under the Variance Gamma model. For near atthemoney options of short maturity, our method is much faster than those based on discretization and truncation of the inverse Fourier transform integral (iFT method). We show that the results calculated with our method agree with those obtained with the iFT algorithm using very long and fine grids. Taking the results of our method as a benchmark, we show that the parabolic modification of the iFT method (Boyarchenko and Levendorskiĭ, 2012) is much more efficient than the standard (flat) version. Based on this conclusion, we consider an approach which uses a combination of backward induction and parabolic iFT to price discretely monitored barrier options, as well as credit default swaps, under wide classes of Lévy models. At each step of backward induction, we use piecewise polynomial interpolation and parabolic iFT, which allows for efficient error control. We derive accurate recommendations for the choice of parameters of the numerical scheme, and produce numerical examples showing that oversimplified prescriptions in other methods can result in large errors.

53 
Particle Approximation in Stochastic FilteringKhalil, Hassan Kamel January 2008 (has links)
The sequential Monte Carlo (SMC) methodology is a family of Monte Carlo methods that processes information sequentially. It has shown to be able to solve a large class of highly complex inference and optimization problems that can be formulated as stochastic dynamic systems. By recursively generating random samples of the state variables of the dynamic systems, SMC adapts flexibly to the dynamics of the underlying stochastic systems. It opens up new frontiers for crossfertilization between statistical science and many application areas.

54 
Advanced stochastic approximation frameworks and their applicationsPerkins, Steven January 2013 (has links)
This thesis makes two extensions to the standard stochastic approximation framework in order to study learning algorithms in different environments. In particular, the aim of this has been to study fictitious play and stochastic fictitious play in more complex frameworks than the usual, normal form game environment. However, these stochastic approximation frameworks are also utilised in other applications in this thesis. A new twotimescale asynchronous stochastic approximation framework with setvalued updates is presented, which extends the previous work in this area by Konda and Borkar (2000). Using this approach a twotimescales learning algorithm is produced for discounted reward Markov decision processes and, similarly, fictitious play is studied in stochastic games. In the second half of this thesis an update to the existing abstract stochastic approximation framework based on the asymptotic pseudotrajectory approach of Benaim (1999), is presented. Importantly, in this thesis criteria are given to control the noise term associated with this abstract stochastic approximation for certain useful Banach spaces. The logit best response dynamic has previously been studied in continuous action games by Lahkar and Riedel (2013). Their existence results are extended for the Nplayer case and a convergence result is proved for twoplayer zerosum games with continuous actions sets. Stochastic fictitious play is then studied using abstract stochastic approximation and is shown to converge to a logit equilibrium strategy in twoplayer zerosum games with continuous action sets . The final chapter of this thesis studies Newton's algorithm, which can be used as a computationally efficient method for estimating a mixing density in a mixture model. Tokdar et al. (2009) give certain conditions for this algorithm to converge to the true mixing density when the parameter space is an uncountable subset of R. One of their assumptions is removed and the convergence result strengthened to produce an alternative consistency result for Newton's Algorithm.

55 
Stochastic control for spectrally negative Lévy processesLoeffen, Ronnie Lambertus January 2008 (has links)
Three optimal dividend models are considered for which the underlying risk process is a spectrally negative Levy process. The first one concerns the classical dividends problem of de Finetti for which we give sufficient conditions under which the optimal strategy is of barrier type. As a consequence, we are able to extend considerably the class of processes for which the barrier strategy proves to be optimal.

56 
Stable processWatson, Alexander Rhys January 2013 (has links)
We consider several first passage problems for stable processes, giving explicit formulas for hitting distributions, hitting probabilities and potentials of stable processes killed at first passage. Our principal tools are the Lamperti representation of positive selfsimilar Markov processes and the WienerHopf factorisation of Levy processes. As part of the proof apparatus, we introduce a new class of Levy processes with explicit Wiener Hopf factorisation, which appear repeatedly in Lamperti representations derived from stable processes. We also apply the LampertiKiu representation of real selfsimilar Markov processes and obtain results on the exponential functional of Markov additive processes, in order to find the law of the first time at which a stable process reaches the origin.

57 
Inference processes for probabilistic first order languagesRad, Soroush Rafiee January 2009 (has links)
In this thesis we will investigate inference processes for predicate languages. The main question we are concerned with in this thesis is how to choose a probability function amongst those that satisfy a certain knowledge base. This question has been extensively studied for propositional logic and we shall investigate it for first order languages. We will first study the generalisation of Minimum Distance. MD. and Centre of Mass. CMco inference processes to unary predicate languages and then we will investigate the generalisations of itie Maximum Entropy inference process to general polyadic languages. For the case of the Maximum Entropy inference process we will study and compare two generalisations. the BPmethod and the Wmethod. We will show that the two methods agree for the unary and :E, knowledge bases and we conjecture that the result holds for the II, knowledge bases too. We shall show that neither of these generalisations for the Maximum Entropy inference process is universally well defined for a first order language and we shall study some of the problems associated with generalising this inference process to polyadic languages.

58 
High gain control of stochastic differential equationsMatsikis, Iakovos January 2004 (has links)
No description available.

59 
Optimal generalised measurement strategiesHunter, Kieran January 2004 (has links)
No description available.

60 
Numerical algorithms for the calculation of finite time ruin probabilities in generalisations of the classical risk modelCardoso, Rui Manuel Rodrigues January 2004 (has links)
No description available.

Page generated in 0.03 seconds