Tomasz Rolski – författare

In this set of notes we study a notion of a random process assoc- ted with a point process. The presented theory was inSpired by q- ueing problems. However it seems to be of interest in other branches of applied probability, as for example reliability or dam theory. Using developed tools, we work out known, aswell as new results from queueing or dam theory. Particularly queues which cannot be treated by standard techniques serve as illustrations of the theory. In Chapter 1 the preliminaries are given. We acquaint the reader with the main ideas of these notes, introduce some useful notations, concepts and abbreviations. He also recall basic facts from ergodic theory, an important mathematical tool employed in these notes. Finally some basic notions from queues are reviewed. Chapter 2 deals with discrete time theory. It serves two purposes. The first one is to let the reader get acquainted with the main lines of the theory needed in continuous time without being bothered by tech­ nical details. However the discrete time theory also seems to be of interest itself. There are examples which have no counte~ in continuous time. Chapter 3 deals with continuous time theory. It also contains many basic results from queueing or dam theory. Three applications of the continuous time theory are given in Chapter 4. We show how to use the theory in order to get some useful bounds for the stationary distribution of a random process.

The Wiley Paperback Series makes valuable content more accessible to a new generation of statisticians, mathematicians and scientists.

Stochastic Processes for Insurance and Finance offers a thorough yet accessible reference for researchers and practitioners of insurance mathematics. Building on recent and rapid developments in applied probability the authors describe in general terms models based on Markov processes, martingales and various types of point processes.

Discussing frequently asked insurance questions, the authors present a coherent overview of this subject and specifically address:

the principle concepts of insurance and finance practical examples with real life data numerical and algorithmic procedures essential for modern insurance practices

Assuming competence in probability calculus, this book will provide a rigorous treatment of insurance risk theory recommended for researchers and students interested in applied probability as well as practitioners of actuarial sciences.

"An excellent text."—Australian & New Zealand Journal of Statistics

The Wiley Paperback Series makes valuable content more accessible to a new generation of statisticians, mathematicians and scientists.Stochastic Processes for Insurance and Finance offers a thorough yet accessible reference for researchers and practitioners of insurance mathematics. Building on recent and rapid developments in applied probability the authors describe in general terms models based on Markov processes, martingales and various types of point processes.Discussing frequently asked insurance questions, the authors present a coherent overview of this subject and specifically address: the principle concepts of insurance and financepractical examples with real life datanumerical and algorithmic procedures essential for modern insurance practicesAssuming competence in probability calculus, this book will provide a rigorous treatment of insurance risk theory recommended for researchers and students interested in applied probability as well as practitioners of actuarial sciences."An excellent text."—Australian & New Zealand Journal of Statistics

The Wiley Paperback Series makes valuable content more accessible to a new generation of statisticians, mathematicians and scientists.Stochastic Processes for Insurance and Finance offers a thorough yet accessible reference for researchers and practitioners of insurance mathematics. Building on recent and rapid developments in applied probability the authors describe in general terms models based on Markov processes, martingales and various types of point processes.Discussing frequently asked insurance questions, the authors present a coherent overview of this subject and specifically address: the principle concepts of insurance and financepractical examples with real life datanumerical and algorithmic procedures essential for modern insurance practicesAssuming competence in probability calculus, this book will provide a rigorous treatment of insurance risk theory recommended for researchers and students interested in applied probability as well as practitioners of actuarial sciences."An excellent text."—Australian & New Zealand Journal of Statistics

In this set of notes we study a notion of a random process assoc- ted with a point process. The presented theory was inSpired by q- ueing problems. However it seems to be of interest in other branches of applied probability, as for example reliability or dam theory. Using developed tools, we work out known, aswell as new results from queueing or dam theory. Particularly queues which cannot be treated by standard techniques serve as illustrations of the theory. In Chapter 1 the preliminaries are given. We acquaint the reader with the main ideas of these notes, introduce some useful notations, concepts and abbreviations. He also recall basic facts from ergodic theory, an important mathematical tool employed in these notes. Finally some basic notions from queues are reviewed. Chapter 2 deals with discrete time theory. It serves two purposes. The first one is to let the reader get acquainted with the main lines of the theory needed in continuous time without being bothered by tech­ nical details. However the discrete time theory also seems to be of interest itself. There are examples which have no counte~ in continuous time. Chapter 3 deals with continuous time theory. It also contains many basic results from queueing or dam theory. Three applications of the continuous time theory are given in Chapter 4. We show how to use the theory in order to get some useful bounds for the stationary distribution of a random process.

This book presents a broad range of computational techniques based on repeated random sampling, widely known as Monte Carlo methods and sometimes as stochastic simulation. These methods bring together ideas from probability theory, statistics, computer science, and statistical physics, providing tools for solving problems in fields such as operations research, biotechnology, and finance.Topics include the generation and analysis of pseudorandom numbers (which are intended to imitate truly random numbers on a computer), the design and justification of Monte Carlo algorithms, and advanced approaches such as Markov chain Monte Carlo and stochastic optimization. In contrast to deterministic numerical methods, the outcome of a Monte Carlo algorithm is itself random – and one needs the tools of probability and statistics to interpret these results meaningfully. The theoretical foundations, particularly the law of large numbers and central limit theorem, are combined with practical algorithms that reveal both the strengths and subtleties of stochastic simulation.The book includes numerous exercises, both theoretical and computational. Each chapter features step-by-step algorithms, illustrated examples, and results presented through numerical computations, tables, and a variety of plots and figures. All Python code used to produce these results is publicly available, allowing readers to reproduce and explore simulations on their own.Intended primarily for graduate students and researchers, the exposition focuses on core concepts and intuitive understanding, avoiding excessive formalism. The book is suitable both for self-study and as a course text and offers a clear pathway from foundational principles to modern applications.