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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. More generally speaking, stochastic computing represents numbers as streams of random bits and reconstructs numbers by calculating frequencies. The computations are performed on the streams and translate complicated operations on p and q into simple operations on their stream representations. (Because of the method of reconstruction, devices that perform these operations are sometimes called stochastic averaging processors.) In modern terms, stochastic computing can be viewed as an interpretion of calculations in probabilistic terms, which are then evaluated with a Gibbs sampler.

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The book has discussed Stochastic Models to understand the processes of metabolism of glucose and insulin more specific to diabetic patients. This study mainly focuses on assessment of glucose/insulin levels through stochastic modeling approach for Type2-diabetes mellitus patients. It also consists of the mechanism of measuring the dynamics of glucose and insulin levels along with the factors like intake of diet, usage of external insulin and physical activity. Measuring the levels of both glucose/insulin through Markov point process is the core area of study. Further, the study has focused on the solving simultaneous differential equations and achieving the approximate values through numerical methods as the model has limitations in getting classical and abstract solutions. The study has many other focusing issues like consumption patterns of average number of glucose molecules and insulin granules in the blood stream. This study has a good scope of usage in health care industry by developing the suitable interface by converting all these mathematical models as user friendly devices by developing relevant computer software and data visualizations methodologies.

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In the last few years, a re?ned pricing of corporate securities has come intofocusofacademicsandpractitioners.Asempiricalresearchshowed, traditionalassetpricingmodelscouldnotpricecorporatesecuritiess- ?ciently well. Time series properties of quoted securities were di?cult to replicate. In the search for more advanced models that capture the empirical ?ndings, researchers followed two approaches. The ?rst stream of - search ?tted the time series properties of corporate securities directly. Werefertothisclassofmodelsasbeingofreducedform.Securityprices are assumed to follow more advanced stochastic models, in particular 1 models withe.g. non-constant volatility. All studiesofthistypedonot consider the economics of the issuing companies but simply assume a stochastic behavior of the security or its state variables. In contrast, a second, economic literature developed by studying the ?rm. We call these kinds of models structural because the limited liability of equity holders is modeled explicitly as a function of ?rm value. One problem of the reduced form approach is its di?culty of int- pretation in an economic sense. Being technically advanced, reduced form models often lack an intuitive economic model and especially d- guise the economic assumptions. If security pricing is the only purpose of the exercise, we might not need an economic model. However, if we wanttounderstandpricemovements,aseriouslinkwiththeunderlying economics appears important. Thecreditriskliteratureevenadoptedthisparticularterminologyto 2 categorize its models. Whereas reduced form models take each corpo- 1 See e.g. Stein and Stein (1991) for a stochastic volatility model and Heston and Nandi (2000) on GARCH option pricing.

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Volume 1: (edited by Keith W. Hipel) In this landmark collection of papers, highly respected scientists and engineers from around the world present the latest research results in extreme value analyses for floods and droughts. Two approaches that are commonly employed in flood frequency analyses are the maximum annual flood and partial duration series or peak over threshold procedures. Recent theoretical advances as well as illustrative applications are described in detail for each of these approaches. Additionally, droughts and storms are systematically studied using appropriate probabilistic models. A major part of the volume is devoted to frequency analyses and fitting extreme value distributions to hydrological data. Other thought-provoking topics include regionalization techniques, distributed models, entropy and fractal analysis. Volume 1 is of interest to researchers, teachers, students and practitioners who wish to place themselves at the leading edge of flood frequency and drought analyses. Volume 2: (edited by Keith W. Hipel) World renowned scientists present valuable contributions to stochastic and statistical modelling of groundwater and surface water systems. The philosophy of probabilistic modelling in the hydrological sciences is put into proper perspective and the importance of stochastic differential equations in the environmental sciences is explained and illustrated. The new research ideas put forward in groundwater modelling will assist decision makers in tackling challenging problems such as controlling pollution of underground aquifers and obtaining adequate water supplies. Additionally, different types of stochastic models are used in modelling a range of interesting surface water problems. Other topics covered in this landmark volume include stochastic optimization, moment analysis, carbon dioxide modelling and rainfall prediction. Volume 2 is of interest to researchers, teachers, students and practitioners who wish to be at the leading edge of stochastic and statistical modelling in the environmental sciences. Volume 3: (edited by Keith W. Hipel, A. Ian McLeod, U.S. Panu, Vijay P. Singh) International experts from around the globe present a rich variety of intriguing developments in time series analysis in hydrology and environmental engineering. Climatic change is of great concern to everyone and significant contributions to this challenging research topic are put forward by internationally renowned authors. A range of interesting applications in hydrological forecasting are given for case studies in reservoir operation in North America, Asia and South America. Additionally, progress in entropy research is described and entropy concepts are applied to various water resource systems problems. Neural networks are employed for forecasting runoff and water demand. Moreover, graphical, nonparametric and parametric trend analyses methods are compared and applied to water quality time series. Other topics covered in this landmark volume include spatial analyses, spectral analyses and different methods for stream-flow modelling. Volume 3 constitutes an invaluable resource for researchers, teachers, students and practitioners who wish to be at the forefront of time series analysis in the environmental sciences. Volume 4: (edited by Keith W. Hipel, Liping Fang) In this landmark set of papers, experts from around the world present the latest and most promising approaches to both the theory and practice of effective environmental management. To achieve sustainable development, organizations and individual citizens must comply with environmental laws and regulations. Accordingly, a major contribution of this book is the presentation of original techniques for designing effective environmental policies, regulations, inspection procedures and monitoring systems. Interesting methods for modelling risk and decision making problems are discussed from an environmental management perspective. Moreover, knowledge-base

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Software reliability is one of the most important characteristics of software product quality. Its measurement and management technologies during the software product life cycle are essential to produce and maintain quality/reliable software systems.Part 1 of this book introduces several aspects of software reliability modeling and its applications. Hazard rate and nonhomogeneous Poisson process (NHPP) models are investigated particularly for quantitative software reliability assessment. Further, imperfect debugging and software availability models are discussed with reference to incorporating practical factors of dynamic software behavior. Three software management problems are presented as application technologies of software reliability models: the optimal software release problem, the statistical testing-progress control, and the optimal testing-effort allocation problem.Part 2 of the book describes several recent developments in software reliability modeling and their applications as quantitative techniques for software quality/reliability measurement and assessment. The discussion includes a quality engineering analysis of human factors affecting software reliability during the design review phase, which is the upper stream of software development, as well as software reliability growth models based on stochastic differential equations and discrete calculus during the testing phase, which is the lower stream. The final part of the book provides an illustration of quality-oriented software management analysis by applying the multivariate analysis method and the existing software reliability growth models to actual process monitoring data.

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Markov processes represent a universal model for a large variety of real life random evolutions. The wide flow of new ideas, tools, methods and applications constantly pours into the ever-growing stream of research on Markov processes that rapidly spreads over new fields of natural and social sciences, creating new streamlined logical paths to its turbulent boundary. Even if a given process is not Markov, it can be often inserted into a larger Markov one (Markovianization procedure) by including the key historic parameters into the state space. This monograph gives a concise, but systematic and self-contained, exposition of the essentials of Markov processes, together with recent achievements, working from the "physical picture"- a formal pre-generator, and stressing the interplay between probabilistic (stochastic differential equations) and analytic (semigroups) tools. The book will be useful to students and researchers. Part I can be used for a one-semester course on Brownian motion, Lévy and Markov processes, or on probabilistic methods for PDE. Part II mainly contains the author's research on Markov processes. From the contents: Tools from Probability and Analysis Brownian motion Markov processes and martingales SDE, ψDE and martingale problems Processes in Euclidean spaces Processes in domains with a boundary Heat kernels for stable-like processes Continuous-time random walks and fractional dynamics Complex chains and Feynman integral

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Anbieter: Orell Fuessli CH

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It is the main purpose of the book to give a logically consistent foundation of migration decision making under incomplete information in a unified framework. Decision rules for migration are derived from a general model of Stochastic Dynamic Programming and the properties of temporary migration equilibria are discussed as well. Finally, some hints are given for esti- mating the theoretical models which are elaborated in the book. Many results concerning the properties of optimal migration policies and of temporary migration equilibria are new. For example, it is demonstrated that less information about a country might it make more attractive for immigration, and conditions are analyzed that imply the existence of a significant stream of migrants even between identical countries in a temporary equilibrium state. The book is written for the mathematically oriented reader in economics, operations research or econometrics who is interested in application of Stochastic Dynamic Programming to an important field of research in population economics.

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Software reliability is one of the most important characteristics of software product quality. Its measurement and management technologies during the software product life cycle are essential to produce and maintain quality/reliable software systems. Part 1 of this book introduces several aspects of software reliability modeling and its applications. Hazard rate and nonhomogeneous Poisson process (NHPP) models are investigated particularly for quantitative software reliability assessment. Further, imperfect debugging and software availability models are discussed with reference to incorporating practical factors of dynamic software behavior. Three software management problems are presented as application technologies of software reliability models: the optimal software release problem, the statistical testing-progress control, and the optimal testing-effort allocation problem. Part 2 of the book describes several recent developments in software reliability modeling and their applications as quantitative techniques for software quality/reliability measurement and assessment. The discussion includes a quality engineering analysis of human factors affecting software reliability during the design review phase, which is the upper stream of software development, as well as software reliability growth models based on stochastic differential equations and discrete calculus during the testing phase, which is the lower stream. The final part of the book provides an illustration of quality-oriented software management analysis by applying the multivariate analysis method and the existing software reliability growth models to actual process monitoring data.

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