Excessive functions, Appell polynomials and optimal stopping

The main topic of the thesis is optimal stopping. This is treated in two research articles. In the first article we introduce a new approach to optimal stopping of general strong Markov processes. The approach is based on the representation of excessive functions as expected suprema. We present a variety of examples, in particular, the Novikov-Shiryaev problem for Lévy processes. In the second article on optimal stopping we focus on differentiability of excessive functions of diffusions and apply these results to study the validity of the principle of smooth fit. As an example we discuss optimal stopping of sticky Brownian motion. The third research article offers a survey like discussion on Appell polynomials. The crucial role of Appell polynomials in optimal stopping of Lévy processes was noticed by Novikov and Shiryaev. They described the optimal rule in a large class of problems via these polynomials. We exploit the probabilistic approach to Appell polynomials and show that many classical results are obtained with ease in this framework. In the fourth article we derive a new relationship between the generalized Bernoulli polynomials and the generalized Euler polynomials.

The theory of classical Greek music

Luettelointi kesken

MCMC Analysis Of Classical Time Series Algorithms

Identification of order of an Autoregressive Moving Average Model (ARMA) by the usual graphical method is subjective. Hence, there is a need of developing a technique to identify the order without employing the graphical investigation of series autocorrelations. To avoid subjectivity, this thesis focuses on determining the order of the Autoregressive Moving Average Model using Reversible Jump Markov Chain Monte Carlo (RJMCMC). The RJMCMC selects the model from a set of the models suggested by better fitting, standard deviation errors and the frequency of accepted data. Together with deep analysis of the classical Box-Jenkins modeling methodology the integration with MCMC algorithms has been focused through parameter estimation and model fitting of ARMA models. This helps to verify how well the MCMC algorithms can treat the ARMA models, by comparing the results with graphical method. It has been seen that the MCMC produced better results than the classical time series approach.

Orthogonal function method in modelling paper web quality variation

This work is devoted to the analysis of signal variation of the Cross-Direction and Machine-Direction measurements from paper web. The data that we possess comes from the real paper machine. Goal of the work is to reconstruct the basis weight structure of the paper and to predict its behaviour to the future. The resulting synthetic data is needed for simulation of paper web. The main idea that we used for describing the basis weight variation in the Cross-Direction is Empirical Orthogonal Functions (EOF) algorithm, which is closely related to Principal Component Analysis (PCA) method. Signal forecasting in time is based on Time-Series analysis. Two principal mathematical procedures that we used in the work are Autoregressive-Moving Average (ARMA) modelling and Ornstein–Uhlenbeck (OU) process.

Non-Markovian Dynamics and the Quantum-To-Classical Transition for Quantum Brownian Motion

In this Thesis I discuss the dynamics of the quantum Brownian motion model in harmonic potential. This paradigmatic model has an exact solution, making it possible to consider also analytically the non-Markovian dynamics. The issues covered in this Thesis are themed around decoherence. First, I consider decoherence as the mediator of quantum-to-classical transition. I examine five different definitions for nonclassicality of quantum states, and show how each definition gives qualitatively different times for the onset of classicality. In particular I have found that all characterizations of nonclassicality, apart from one based on the interference term in the Wigner function, result in a finite, rather than asymptotic, time for the emergence of classicality. Second, I examine the diverse effects which coupling to a non-Markovian, structured reservoir, has on our system. By comparing different types of Ohmic reservoirs, I derive some general conclusions on the role of the reservoir spectrum in both the short-time and the thermalization dynamics. Finally, I apply these results to two schemes for decoherence control. Both of the methods are based on the non-Markovian properties of the dynamics.

Winning time in land warfare : a reading of the classical strategists prior to the age of mechanization

We live in an age where rationalization and demands of efficiency taint every aspect of our lives both as individuals and as a society. Even warfare cannot escape the increased speed of human interaction. Time is a resource to be managed. It has to be optimized, saved and won in military affairs as well. The purpose of this research paper is to analyze the dogmatic texts of military thought to search for answers what the classics of strategy saw in the interrelations of temporality and warfare and if their thoughts remain meaningful in the contemporary conjunction. Since the way a society functions is reflected in the way it conducts its wars, there naturally are differences between an agrarian, industrial and information society. Theorists of different eras emphasize things specific to their times, but warfare, like any human interaction, is always bounded by temporality. Not only is the pace of warfare dependent on the progress of the society, but time permeates warfare in all its aspects. This research paper focuses on two specific topics that arose from the texts themselves; how should time be managed and manipulated in warfare and how to economize and “win” it from the enemy. A method where lengthy quotations are used to illustrate the main point of the strategists has been chosen for this research paper. While Clausewitz is the most prominent source of quotations, thoughts from ancient India and China are represented as well to prove that the combination of right force in the right place at the right time is still the way of the victorious. Tactics change in the course of time but the principles of strategy remain unaltered and are only adapted to suit new situations. While ancient and pre-modern societies had their focus on finding auspicious moments for battle in the flow of kronos-time based on divinities, portents and auguries, we can trace elements of manipulation of time in warfare from the earliest surviving texts. While time as a fourth dimension of the battlespace emerged only in the modern era, all through the history of military thought it has had a profound meaning. In the past time could be squandered, today it always has to be won. This paper asks the question “why”.