الصفحة 1
الصفحة 1
Introductory Lectures on Fluctuations of Lévy Processes with Applications
Lévy processes are the natural continuous-time analogue of random walks and form a rich class of stochastic processes around which a robust mathematical theory exists. Their mathematical significance is justified by their application in many areas of classical and modern stochastic models including storage models, renewal processes, insurance risk models, optimal stopping problems, mathematical finance and continuous-state branching processes.The book aims to be mathematically rigorous while still providing an intuitive feel for underlying principles. The results and applications often focus on the case of Lévy processes with jumps in only one direction.
Interacting Stochastic Systems
The Research Network on "Interacting stochastic systems of high complexity" set up by the German Research Foundation aimed at exploring and developing connections between research in infinite-dimensional stochastic analysis, statistical physics, spatial population models from mathematical biology, complex models of financial markets or of stochastic models interacting with other sciences. This book presents a structured collection of papers on the core topics, written at the close of the 6-year programme by the research groups who took part in it. The structure chosen highlights the interweaving of certain themes and certain interconnections discovered through the joint work.
Inference for change point and post change means after a CUSUM test
This monograph is the first to systematically study the bias of estimators and construction of corrected confidence intervals for change-point and post-change parameters after a change is detected by using a CUSUM procedure. Researchers in change-point problems and sequential analysis, time series and dynamic systems, and statistical quality control will find that the methods and techniques are mostly new and can be extended to more general dynamic models where the structural and distributional parameters are monitored. Practitioners, who are interested in applications to quality control, dynamic systems, financial markets, clinical trials and other areas, will benefit from case studies based on data sets from river flow, accident interval, stock prices, and global warming. Readers with an elementary probability and statistics background and some knowledge of CUSUM procedures will be able to understand most results as the material is relatively self-contained.The exponential family distribution is used as the basic model that includes changes in mean, variance, and hazard rate as special cases. There are fundamental differences between the sequential sampling plan and fixed sample size. Although the results are given under the CUSUM procedure, the methods and techniques discussed provide new approaches to deal with inference problems after sequential change-point detection, and they also contribute to the theoretical aspects of sequential analysis. Many results are of independent interests and can be used to study random walk related stochastic models.
Formal Methods and Stochastic Models for Performance Evaluation ; 4th European Performance Engineering Workshop, EPEW 2007, Berlin, Germany, September 27-28, 2007, Proceedings
This book constitutes the refereed proceedings of the 4th European Performance Engineering Workshop, EPEW 2007, held in Berlin, Germany, September 27-28, 2007.The 20 revised full papers presented were carefully reviewed and selected from 53 submissions.
Formal Methods and Stochastic Models for Performance Evaluation ; 3rd European Performance Engineering Workshop, EPEW 2006, Budapest, Hungary, June 21-22, 2006, Proceedings
This volume contains the proceedings of the third EPEW workshop held at the Technical University of Budapest, Budapest, Hungary, June 21-22, 2006. These proceedings comprise the 16 accepted contributed papers of EPEW 2006.Toensurethehigh-qualityevaluationofthesubmittedpapersweextended the ProgramCommittee of EPEW 2006 with international experts from all over the world. The ?nal workshop program, as well as this volume, are made up of ?ve thematic sessions: – Stochastic process algebra – Workloads and benchmarks – Theory of stochastic processes – Formal dependability and performance evaluation – Queues, theory and practice These sessions cover a wide range of performance evaluation methods and c- pose an overview of the current research directions in performance evaluation.
Forecasting with Exponential Smoothing : The State Space Approach
Exponential smoothing methods have been around since the 1950s, and are the most popular forecasting methods used in business and industry. Recently, exponential smoothing has been revolutionized with the introduction of a complete modeling framework incorporating innovations state space models, likelihood calculation, prediction intervals and procedures for model selection. In this book, all of the important results for this framework are brought together in a coherent manner with consistent notation. In addition, many new results and extensions are introduced and several application areas are examined in detail.
Computing Characterizations of Drugs for Ion Channels and Receptors Using Markov Models
Flow of ions through voltage gated channels can be represented theoretically using stochastic differential equations where the gating mechanism is represented by a Markov model. The flow through a channel can be manipulated using various drugs, and the effect of a given drug can be reflected by changing the Markov model. These lecture notes provide an accessible introduction to the mathematical methods needed to deal with these models. They emphasize the use of numerical methods and provide sufficient details for the reader to implement the models and thereby study the effect of various drugs. Examples in the text include stochastic calcium release from internal storage systems in cells, as well as stochastic models of the transmembrane potential. Well known Markov models are studied and a systematic approach to including the effect of mutations is presented.
Mathematical Modeling for the Life Sciences
Proposing a wide range of mathematical models that are currently used in life sciences may be regarded as a challenge, and that is precisely the challenge that this book takes up. Of course this panoramic study does not claim to offer a detailed and exhaustive view of the many interactions between mathematical models and life sciences. This textbook provides a general overview of realistic mathematical models in life sciences, considering both deterministic and stochastic models and covering dynamical systems, game theory, stochastic processes and statistical methods. Each mathematical model is explained and illustrated individually with an appropriate biological example. Finally three appendices on ordinary differential equations, evolution equations, and probability are added to make it possible to read this book independently of other literature.
Mathematical and Statistical Methods in Insurance and Finance
The interaction between mathematicians and statisticians reveals to be an effective approach to the analysis of insurance and financial problems, in particular in an operative perspective. The Maf2006 conference, held at the University of Salerno in 2006, had precisely this purpose and the collection here published gathers some of the papers presented at the conference and successively worked out to this aim. They cover a wide variety of subjects in insurance and financial fields, all treated in light of the successful cooperation between the two quantitative methods.
Level Crossing Methods in Stochastic Models
Since its inception in 1974, the level crossing approach for analyzing a large class of stochastic models has become increasingly popular among researchers. This volume traces the evolution of level crossing theory for obtaining probability distributions of state variables and demonstrates solution methods in a variety of stochastic models including: queues, inventories, dams, renewal models, counter models, pharmacokinetics, and the natural sciences. Results for both steady-state and transient distributions are given, and numerous examples help the reader apply the method to solve problems faster, more easily, and more intuitively.
Complexity hints for economic policy
This volume extends the complexity approach to economics. It provides some alternative pattern generators, which can supplement existing approaches by providing an alternative way of finding patterns than be obtained by the traditional scientific approach.
Advanced Reliability Models and Maintenance Policies
Advanced Reliability Models and Maintenance Policies introduces partition and redundant problems within reliability models, and provides optimization techniques. The book also indicates how to perform maintenance in a finite time span and at failure detection, and to apply recovery techniques for computer systems.
