This thesis consists of four papers, all concerning random iteration of isometries. The papers are: I. Ambroladze A, Ådahl M, Random iteration of isometries in unbounded metric spaces. Nonlinearity 16 (2003) 1107-1117. II. Ådahl M, Random iteration of isometries controlled by a Markov chain. Manuscript. III. Ådahl M, Melbourne I, Nicol M, Random iteration of Euclidean isometries. Nonlinearity 16 (2003) 977-987. IV. Johansson A, Ådahl M, Recurrence of a perturbed random walk and an iterated function system depending on a parameter. Manuscript. In the first paper we consider an iterated function system consisting of isometries on an unbounded metric space. Under suitable conditions it is proved that the random orbit {Zn} ∞n=0, of the iterations corresponding to an initial point Z0, “escapes to infinity" in the sense that P(Zn Є K) → 0, as n → ∞ for every bounded set K. As an application we prove the corresponding result in the Euclidean and hyperbolic spaces under the condition that the isometries do not have a common fixed point. In the second paper we let a Markov chain control the random orbit of an iterated function system of isometries on an unbounded metric space. We prove under necessary conditions that the random orbit \escapes to infinity" and we also give a simple geometric description of these conditions in the Euclidean and hyperbolic spaces. The results generalises the results of Paper I. In the third paper we consider the statistical behaviour of the reversed random orbit corresponding to an iterated function system consisting of a finite number of Euclidean isometries of <b>R</b>n. We give a new proof of the central limit theorem and weak invariance principles, and we obtain the law of the iterated logarithm. Our results generalise immediately to Markov chains. Our proofs are based on dynamical systems theory rather than a purely probabilistic approach. In the fourth paper we obtain a suficient condition for the recurrence of a perturbed (one-sided) random walk on the real line. We apply this result to the study of an iterated function system depending on a parameter and defined on the open unit disk in the complex plane.

Många berättar om de ekonomiska vinster de gjort på börsen under senaste åren, och hur lätt pengarna rullat in på deras konton. Med en liten inblick i finansmarknaden och genom att titta på A-ekonomi då och då så blir i stort sett alla aktieaffärer lyckade. Vi hör dock sällan någon berätta om folks dåliga aktieaffärer. Börsen verkar med andra ord vara en guldgruva för dem som investerar där. Med hjälp av dyra aktierekommendationer kan man göra ännu större vinster enligt en rad olika fondkommissionär. Betting är en trend som aldrig tycks ta slut. Även där påpekar spelbolagen hur lätt det är att ta hem vinster, bara man har lite kunskap blir man en vinnare. Och vem vill inte bli det? Syftet med denna uppsats är att reda ut nämnda påstående. Är det så lätt som visa försöker påvisa att öka sina likvida medel med hjälp av en smärre aktiekunskap? Denna studie försöker visa hur det egentligen ligger till i denna fråga. Vem vinner när kunskap ställs mot slump i spel- och aktievärlden? I denna uppsats vill vi undersöka likheterna av slumpens betydelse vid kortsiktiga placeringar i aktier och spel på multibet. Med hjälp av Random Walk-teorin vill vi se om det finns likheter mellan att köpa aktier på börsen och att spela på multibet. För att få en bredare kunskap inom detta ämne så har vi byggt upp en teoridel i denna uppsats som tar upp elementära och relevanta grundstenar inom dessa ämnen. Det dyker upp en rad olika frågetecken under resans gång, men dessa försöker vi besvara så gott det går ännu längre fram i uppsatsen. De slutsatser vi kommit fram till med hjälp av vår undersökning är att slumpen har en stor betydelse på aktie- respektive spelmarknaden. Men däremot tror vi inte att den tekniska och fundamentala analysen ska förkastas, den kan i viss mån vara till hjälp.

Even though today´s world unwinds on the increasing way of the globalisation, investors are aware of the possibilities the international markets offer and distance is not an issue any more, they are still governed by the “home bias factor“. This phenomenon implies that investors tend to prefer investing in domestic securities rather than entering the global market. Swedish investors are not the exception and the issue of the attraction of foreign fixed income securities is highlighted even more when we have found out there is lack of academic research about the topic from the perspective of Swedish investors. To narrow down the research subject and provide a reader with an interesting approach, we decided to examine the attraction of foreign government bonds from the perspective of Swedish investors. At the beginning of the paper we raised three research questions and defined the objective of the paper in questioning the existence of reasons to invest in foreign government bonds. Another research question was defined as identifying our local investor, who is entering the global market and last, but not least, what investing strategy do we recommend him to follow. Along the paper we proposed to apply a decent level of informative as well as a scientific approach to provide a reader with a valuable study concerning pre-defined topic. To reach more concrete outcomes of the study we have accepted couple of assumtions which we have identified ourselves with and we have stressed them especially during the theoretical part of the paper. After conducting the comprehensive analysis of the Swedish market for government bonds we have identified a huge gap between the demand and supply for such bonds and based on the discussion concerning the opportunities and risks connected with such investments we have defined our investor. Under given assumptions, as the most probable case of occurance we consider a rational investor, who is offsetting the balance of interest rate sensitive assets and liabilities simultaneously looking for the best possible yield, the lowest possible risk and sound level of diversification. During the empirical analysis, namely examination of the national yield curves we set first, however very limited investment strategy. After the incorporation of the portfolio theory, currency rate risk and the existence of instruments covering the foreign currency exposure we have come into a conclusion that our investor does not have to necessarily prefer a security from the depicted efficient frontier, but he can employ other securities as well. As a consequence, when using 100% hedging he can use whichever security on the global market. At the conclusion, stated findings imply another investigation, since our research was based on very strong assumptions presented during the study. Thus it by far does not provide the reader with a comprehensive investment analysis, which some readers might be interested in. However, even from the beginning we claimed that we do not have such an ambitious goal.

This thesis concerns computer simulation of diffusional processes in alloys. The main focus is on the development of simulation techniques for diffusion in single-phase domains, but also diffusion controlled phase-transformations and interfacial processes are discussed. Different one-dimensional simulation techniques for studying the Kirkendall effect are developed and analyzed. Comparisons with experimentally observed marker migration show good agreement for small shifts and comparisons with observed Kirkendall porosity show reasonable agreement under the assumption that a certain supersaturation is needed before the vacancies coalesce into pores. A convenient approach in simulations of kinetics is to use thermodynamic software, e.g. Thermo-Calc, to calculate thermodynamic quantities, e.g. chemical potentials, required in the simulation. The main drawback with such an approach is that it will generate a large amount of additional computational work. To overcome this problem a method that decreases the amount of computational work has been developed. The new method is based on artificial neural networks (ANN). By training the ANN to estimate thermodynamic quantities a significant increase in computational speed was obtained. By calculating the dissipation of available driving force due to diffusion inside migrating interfaces an approach for including the effect of solute drag in computer simulations of grain growth and phase transformations has been developed. The new method is based on an effective interfacial mobility and simulations of grain growth have been performed in binary and ternary systems using experimentally assessed model parameters. / QC 20100930

<p>Evolutionary dynamics can be notoriously complex and difficult to analyze. In this dissertation I describe a population genetic regime where the dynamics are simple enough to allow a relatively complete and elegant treatment. Consider a haploid, asexual population, where each possible genotype has been assigned a fitness. When mutations enter a population sufficiently rarely, we can model the evolution of this population as a Markov chain where the population jumps from one genotype to another at the birth of each new mutant destined for fixation. Furthermore, if the mutation rates are assigned in such a manner that the Markov chain is reversible when all genotypes are assigned the same fitness, then it is still reversible when genotypes are assigned differing fitnesses. </p><p>The key insight is that this Markov chain can be analyzed using the spectral theory of finite-state, reversible Markov chains. I describe the spectral decomposition of the transition matrix and use it to build a general framework with which I address a variety of both classical and novel topics. These topics include a method for creating low-dimensional visualizations of fitness landscapes; a measure of how easy it is for the evolutionary process to `find' a specific genotype or phenotype; the index of dispersion of the molecular clock and its generalizations; a definition for the neighborhood of a genotype based on evolutionary dynamics; and the expected fitness and number of substitutions that have occurred given that a population has been evolving on the fitness landscape for a given period of time. I apply these various analyses to both a simple one-codon fitness landscape and to a large neutral network derived from computational RNA secondary structure predictions.</p> / Dissertation

The purpose of this study is to examine a completely new phenomenon called the MIST, by two portfolios: the Goldman Sachs Next 11 equity fund, and the Goldman Sachs BRIC fund, in order to establish whether or not the MIST countries are a better investment decision in terms of risk, return and growth. Furthermore, the study examines in which form these emerging markets lies in terms of market efficiency, and if the random walk theory is present. The opportunities and challenges for Mexico, Indonesia, South Korea and Turkey are also brought upon to determine whether these countries have the potential to exhibit the same success as the BRIC countries did for a decade. Since the growth of the BRIC countries are slowing down, Jim O’Neill, the same founder of the term BRIC, coined the nations MIST. The BRIC countries are facing several difficulties and have led investors to draw out from these countries stocks. Investors that were pouring in money to the BRIC countries during the period 2001-2009, have from 2011, withdrawn 15 billion dollars from the BRIC stocks. Mexico, Indonesia, South Korea and Turkey. Derived from the next eleven countries, these countries have a major effect on the global economy due to their economical and political circumstances. For many investors, the MIST countries that are growing faster than the BRIC are regarded to be the new biggest emerging markets. Investing in BRIC funds are stated to be a disaster today, while on the other hand, the MIST countries are growing and outpacing the BRIC fund. The methodology used was to compare two different portfolios, Goldman Sachs N-11 equity fund in the period 2011-2013 against the Goldman Sachs BRIC fund in two different periods, 2011-2013 and 2006-2008 with S&amp;P 500 as the market index. In addition, a hypothesis test was carried out for this period to observe whether or not to reject the null hypothesis. The results of this study shows that the null hypothesis was rejected and that the N-11 equity fund is a better investment decision, in terms of risk, return and growth today. These emerging markets are under the weak form market efficiency and the random walk theory is present in the N-11 equity fund. This makes the authors’ results more of a speculation than a definite conclusion about the future, as one cannot "beat the market".

Rotundus AB är ett världsledande företag inom området för sfäriska robotar som håller på att utveckla den markbundna farkosten GroundBot(tm). För att detektera robotens translations- och rotationsrörelser används accelerometrar och hastighetsgyron. Dessutom används sensorerna för tröghetsnavigering när GPS-täckning saknas. Målet med projektet innebär att ta fram en metod för att utvärdera precisionen hos sensorer för robotens tröghetsnavigeringsenhet. Metoden koncentrerar sig på fyra av sensorernas felkällor: Skalfaktor, bias, slumpvandring och biasinstabilitet. För att beräkna skalfaktorn och biasen används linjära minsta kvadratmetoden där utsignalen från sensorn anpassas mot ett teoretiskt värde. Slumpvandringen och biasinstabiliteten utvärderas med Allans varians.

The fast-growing economy in China attracts the world’s interests, which includes the Chinese stock markets. The market efficiency of Chinese stock markets is widely discussed by researchers in different approaches. The involvement of government in stock markets is a unique case in the financial world.   By this paper, we are answering the question that is the degree of market efficiency of stat-owned companies different from that of private companies in Chinese stock markets. This will bring us knowledge about Chinese stock markets as well as the impact from ownership, market value and management styles on market efficiency.   To clarify the influence from government involvement in stock markets, we select 938 stocks distinguished by ownership structure. This quantitative study is preceded on daily data from 2007 to 2011. We use auto correlation, Chi-square test, and linear regression together with Spearman’s correlation to test our hypothesis. The degree of market efficiency of each ownership group is examined and compared to each other. Market efficiency related to ownership and market capitalization are inspected if they are anomaly factors in Chinese markets.   The empirical results indicate that the degree of market efficiency of state-owned companies is significantly different from the degree of market efficiency of private-owned companies in China. The market capitalization is one of the existing anomaly factors in Chinese stock markets, as well as it is correlated with degree of market efficiency to some extent. For state-owned enterprises, active management on stock market does not provide a better market efficiency compared to passively managed companies.

In this study, neutral real interest rate gap and output gap are estimated jointly under two different multivariate unobserved components models with the motivation to provide empirical measures that can be used to analyze the amount of stimulus that monetary policy is passing on to the economy, and to understand historical macroeconomic developments. In the analyses, Kalman filter technique is applied to a small-scale macroeconomic model of the Turkish economy to estimate the unobserved variables for the period 1989-2005. In addition, two alternative specifications for neutral real interest rate are used in the analyses. The first model uses a random walk model for the neutral real interest rate, whereas the second one employs more structural specification, which specifically links the neutral real rate with the trend growth rate and the long-term course of the risk premium. Comparison of the models developed by using various performance criteria clearly indicates the use of more structural specification against random walk specification. Results suggest that though there is relatively high uncertainty surrounding the neutral real interest rate estimates to use them directly in the policy-making process, estimates appear to be very useful for ex-post monetary policy evaluations.

Ziel dieser Arbeit ist die Untersuchung der Dynamik in komplexen Systemen. Eine zentrale Rolle spielen dabei Random Walks, mit deren Hilfe die anomale Relaxation in solchen Systemen simuliert wird. Die Komplexität der in dieser Arbeit untersuchten Systeme spiegelt sich in hohem Maße in deren Zustandsraumstruktur wider. Nach einer Einführung verschiedener komplexer Systeme wird kurz auf Algorithmen eingegangen, die bei der Erfassung der zum Teil sehr großen Zustandsräume eine wichtige Rolle spielen. Ein sogenannter Branch-and-Bound Algorithmus wird für die Untersuchung des niedrigenergetischen Anteils komplexer Zustandsräume eingesetzt. Die Simulation der Dynamik wird durch Random Walk Prozesse simuliert und im Wahrscheinlichkeitsbild durch eine Mastergleichung beschrieben. Auf verschiedene Formen der Mastergleichung und deren Lösung wird detailliert eingegangen. Wichtige Anwendungen sind Simulationen von Random Walks auf Fraktalen bzw. auf hierarchischen Baumstrukturen. Solche Simulationen lassen den Vergleich mit experimentellen Befunden zu, wie z.B. der anomalen Diffusion bzw. den Nichtgleichgewichts- phänomenen in Spingläsern. Anhand einer solchen Modellbildung können experimentelle Ergebnisse reproduziert und besser verstanden werden. Ein weiterer wichtiger Beitrag zum Verständnis solcher Prozesse wird durch einen neu entwickelten Algorithmus zur Vergröberung des Zustandsraumes geleistet.