This thesis consists of five papers. In the first two papers we consider a general approach to cash flow valuation, focusing on dynamic properties of the value of a stream of cash flows. The third paper discusses immunization theory, where old results are shown to hold in general deterministic models, but often fail to be true in stochastic models. In the fourth paper we comment on the connection between arbitrage opportunities and an immunized position. Finally, in the last paper we study coherent and convex measure of risk applied to portfolio optimization and insurance.

<p>The focus of this work is on faults, and the main issue is statistical analysis and stochastic modeling of faults and fault patterns in petroleum reservoirs. The thesis consists of Part I-V and Appendix A-C. The units can be read independently. Part III is written for a geophysical audience, and the topic of this part is fault and fracture size-frequency distributions. The remaining parts are written for a statistical audience, but can also be read by people with an interest in quantitative geology. The topic of Part I and II is statistical model choice for fault size distributions, with a samling algorithm for estimating Bayes factor. Part IV describes work on spatial modeling of fault geometry, and Part V is a short note on line partitioning. Part I, II and III constitute the main part of the thesis. The appendices are conference abstracts and papers based on Part I and IV.</p> / Paper III: reprinted with kind permission of the American Geophysical Union. An edited version of this paper was published by AGU. Copyright [2000] American Geophysical Union

The focus of this work is on faults, and the main issue is statistical analysis and stochastic modeling of faults and fault patterns in petroleum reservoirs. The thesis consists of Part I-V and Appendix A-C. The units can be read independently. Part III is written for a geophysical audience, and the topic of this part is fault and fracture size-frequency distributions. The remaining parts are written for a statistical audience, but can also be read by people with an interest in quantitative geology. The topic of Part I and II is statistical model choice for fault size distributions, with a samling algorithm for estimating Bayes factor. Part IV describes work on spatial modeling of fault geometry, and Part V is a short note on line partitioning. Part I, II and III constitute the main part of the thesis. The appendices are conference abstracts and papers based on Part I and IV. / Paper III: reprinted with kind permission of the American Geophysical Union. An edited version of this paper was published by AGU. Copyright [2000] American Geophysical Union

<p>This thesis consists of five papers. In the first two papers we consider a general approach to cash flow valuation, focusing on dynamic properties of the value of a stream of cash flows. The third paper discusses immunization theory, where old results are shown to hold in general deterministic models, but often fail to be true in stochastic models. In the fourth paper we comment on the connection between arbitrage opportunities and an immunized position. Finally, in the last paper we study coherent and convex measure of risk applied to portfolio optimization and insurance.</p>

<p>The success of the current Internet relies to a large extent on a cooperation between the users and the network. The network signals its current state to the users by marking or dropping packets. The users then strive to maximize the sending rate without causing network congestion. To achieve this, the users implement a flow-control algorithm that controls the rate at which data packets are sent into the Internet. More specifically, the <i>Transmission Control Protocol (TCP)</i> is used by the users to adjust the sending rate in response to changing network conditions. TCP uses the observation of packet loss events and estimates of the round trip time (RTT) to adjust its sending rate. </p><p>In this thesis we investigate and propose stochastic models for TCP. The models are used to estimate network performance like throughput, link utilization, and packet loss rate. The first part of the thesis introduces the TCP protocol and contains an extensive TCP modeling survey that summarizes the most important TCP modeling work. Reviewed models are categorized as renewal theory models, fixed-point methods, fluid models, processor sharing models or control theoretic models. The merits of respective category is discussed and guidelines for which framework to use for future TCP modeling is given. </p><p>The second part of the thesis contains six papers on TCP modeling. Within the renewal theory framework we propose single source TCP-Tahoe and TCP-NewReno models. We investigate the performance of these protocols in both a DropTail and a RED queuing environment. The aspects of TCP performance that are inherently depending on the actual implementation of the flow-control algorithm are singled out from what depends on the queuing environment.</p><p>Using the fixed-point framework, we propose models that estimate packet loss rate and link utilization for a network with multiple TCP-Vegas, TCP-SACK and TCP-Reno on/off sources. The TCP-Vegas model is novel and is the first model capable of estimating the network's operating point for TCP-Vegas sources sending on/off traffic. All TCP and network models in the contributed research papers are validated via simulations with the network simulator <i>ns-2</i>. </p><p>This thesis serves both as an introduction to TCP and as an extensive orientation about state of the art stochastic TCP models.</p>

<p>cDNA microarrays is one of the first high-throughput gene expression technologies that has emerged within molecular biology for the purpose of functional genomics. cDNA microarrays compare the gene expression levels between cell samples, for thousands of genes simultaneously. </p><p>The microarray technology offers new challenges when it comes to data analysis, since the thousands of genes are examined in parallel, but with very few replicates, yielding noisy estimation of gene effects and variances. Although careful image analyses and normalisation of the data is applied, traditional methods for inference like the Student <i>t</i> or Fisher’s <i>F</i>-statistic fail to work.</p><p>In this thesis, four papers on the topics of empirical Bayes and full Bayesian methods for two-channel microarray data (as e.g. cDNA) are presented. These contribute to proving that empirical Bayes methods are useful to overcome the specific data problems. The sample distributions of all the genes involved in a microarray experiment are summarized into prior distributions and improves the inference of each single gene.</p><p>The first part of the thesis includes biological and statistical background of cDNA microarrays, with an overview of the different steps of two-channel microarray analysis, including experimental design, image analysis, normalisation, cluster analysis, discrimination and hypothesis testing. The second part of the thesis consists of the four papers. Paper I presents the empirical Bayes statistic <i>B</i>, which corresponds to a <i>t</i>-statistic. Paper II is based on a version of <i>B</i> that is extended for linear model effects. Paper III assesses the performance of empirical Bayes models by comparisons with full Bayes methods. Paper IV provides extensions of <i>B</i> to what corresponds to <i>F</i>-statistics.</p>

<p>This thesis consists of four papers in domain theory and a summary. The first two papers deal with the problem of defining effectivity for continuous cpos. The third and fourth paper present the new notion of an admissible domain representation, where a domain representation D of a space X is λ-admissible if, in principle, all other λ-based domain representations E of X can be reduced to X via a continuous function from E to D. </p><p>In Paper I we define a cartesian closed category of effective bifinite domains. We also investigate the method of inducing effectivity onto continuous cpos via projection pairs, resulting in a cartesian closed category of projections of effective bifinite domains. </p><p>In Paper II we introduce the notion of an almost algebraic basis for a continuous cpo, showing that there is a natural cartesian closed category of effective consistently complete continuous cpos with almost algebraic bases. We also generalise the notion of a complete set, used in Paper I to define the bifinite domains, and investigate what closure results that can be obtained. </p><p>In Paper III we consider admissible domain representations of topological spaces. We present a characterisation theorem of exactly when a topological space has a λ-admissible and κ-based domain representation. We also show that there is a natural cartesian closed category of countably based and countably admissible domain representations. </p><p>In Paper IV we consider admissible domain representations of convergence spaces, where a convergence space is a set X together with a convergence relation between nets on X and elements of X. We study in particular the new notion of weak κ-convergence spaces, which roughly means that the convergence relation satisfies a generalisation of the Kuratowski limit space axioms to cardinality κ. We show that the category of weak κ-convergence spaces is cartesian closed. We also show that the category of weak κ-convergence spaces that have a dense, λ-admissible, κ-continuous and α-based consistently complete domain representation is cartesian closed when α ≤ λ ≥ κ. As natural corollaries we obtain corresponding results for the associated category of weak convergence spaces.</p>

The success of the current Internet relies to a large extent on a cooperation between the users and the network. The network signals its current state to the users by marking or dropping packets. The users then strive to maximize the sending rate without causing network congestion. To achieve this, the users implement a flow-control algorithm that controls the rate at which data packets are sent into the Internet. More specifically, the Transmission Control Protocol (TCP) is used by the users to adjust the sending rate in response to changing network conditions. TCP uses the observation of packet loss events and estimates of the round trip time (RTT) to adjust its sending rate. In this thesis we investigate and propose stochastic models for TCP. The models are used to estimate network performance like throughput, link utilization, and packet loss rate. The first part of the thesis introduces the TCP protocol and contains an extensive TCP modeling survey that summarizes the most important TCP modeling work. Reviewed models are categorized as renewal theory models, fixed-point methods, fluid models, processor sharing models or control theoretic models. The merits of respective category is discussed and guidelines for which framework to use for future TCP modeling is given. The second part of the thesis contains six papers on TCP modeling. Within the renewal theory framework we propose single source TCP-Tahoe and TCP-NewReno models. We investigate the performance of these protocols in both a DropTail and a RED queuing environment. The aspects of TCP performance that are inherently depending on the actual implementation of the flow-control algorithm are singled out from what depends on the queuing environment. Using the fixed-point framework, we propose models that estimate packet loss rate and link utilization for a network with multiple TCP-Vegas, TCP-SACK and TCP-Reno on/off sources. The TCP-Vegas model is novel and is the first model capable of estimating the network's operating point for TCP-Vegas sources sending on/off traffic. All TCP and network models in the contributed research papers are validated via simulations with the network simulator ns-2. This thesis serves both as an introduction to TCP and as an extensive orientation about state of the art stochastic TCP models.

cDNA microarrays is one of the first high-throughput gene expression technologies that has emerged within molecular biology for the purpose of functional genomics. cDNA microarrays compare the gene expression levels between cell samples, for thousands of genes simultaneously. The microarray technology offers new challenges when it comes to data analysis, since the thousands of genes are examined in parallel, but with very few replicates, yielding noisy estimation of gene effects and variances. Although careful image analyses and normalisation of the data is applied, traditional methods for inference like the Student t or Fisher’s F-statistic fail to work. In this thesis, four papers on the topics of empirical Bayes and full Bayesian methods for two-channel microarray data (as e.g. cDNA) are presented. These contribute to proving that empirical Bayes methods are useful to overcome the specific data problems. The sample distributions of all the genes involved in a microarray experiment are summarized into prior distributions and improves the inference of each single gene. The first part of the thesis includes biological and statistical background of cDNA microarrays, with an overview of the different steps of two-channel microarray analysis, including experimental design, image analysis, normalisation, cluster analysis, discrimination and hypothesis testing. The second part of the thesis consists of the four papers. Paper I presents the empirical Bayes statistic B, which corresponds to a t-statistic. Paper II is based on a version of B that is extended for linear model effects. Paper III assesses the performance of empirical Bayes models by comparisons with full Bayes methods. Paper IV provides extensions of B to what corresponds to F-statistics.

This thesis consists of four papers in domain theory and a summary. The first two papers deal with the problem of defining effectivity for continuous cpos. The third and fourth paper present the new notion of an admissible domain representation, where a domain representation D of a space X is λ-admissible if, in principle, all other λ-based domain representations E of X can be reduced to X via a continuous function from E to D. In Paper I we define a cartesian closed category of effective bifinite domains. We also investigate the method of inducing effectivity onto continuous cpos via projection pairs, resulting in a cartesian closed category of projections of effective bifinite domains. In Paper II we introduce the notion of an almost algebraic basis for a continuous cpo, showing that there is a natural cartesian closed category of effective consistently complete continuous cpos with almost algebraic bases. We also generalise the notion of a complete set, used in Paper I to define the bifinite domains, and investigate what closure results that can be obtained. In Paper III we consider admissible domain representations of topological spaces. We present a characterisation theorem of exactly when a topological space has a λ-admissible and κ-based domain representation. We also show that there is a natural cartesian closed category of countably based and countably admissible domain representations. In Paper IV we consider admissible domain representations of convergence spaces, where a convergence space is a set X together with a convergence relation between nets on X and elements of X. We study in particular the new notion of weak κ-convergence spaces, which roughly means that the convergence relation satisfies a generalisation of the Kuratowski limit space axioms to cardinality κ. We show that the category of weak κ-convergence spaces is cartesian closed. We also show that the category of weak κ-convergence spaces that have a dense, λ-admissible, κ-continuous and α-based consistently complete domain representation is cartesian closed when α ≤ λ ≥ κ. As natural corollaries we obtain corresponding results for the associated category of weak convergence spaces.