http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
Poisson process and its fractional extensions with applications
"This book accompanies the reader from the simple, standard Poisson process to its more complex transformations, using a unified framework, showing proofs of basic theorems and references to more difficult results. The reader benefits also from the empirical applications of the various models to real data in a wide range of fields: physics, geology (earthquakes), biology (pandemic), finance (stock market), insurance (car accidents) etc. Some examples are worked out in open source R to show the reader how to implement the models. The strengths of the book are: i) the focus on a very fundamental class of stochastic processes; ii) the introductory approach; iii) the wide range of generalizations considered, including recent advances, to which one of the authors has made seminal contributions; iv) and the attention not only to theory but also to practical applications, with real-data examples from a wide range of fields"-- Provided by publisher.
Cover -- Half Title -- Series Page -- Title Page -- Copyright Page -- Contents -- Symbols -- Preface -- About the Authors -- I. Poisson processes -- 1. Poisson Processes -- 1.1. The Homogeneous Poisson Process -- 1.1.1. Properties of the Homogeneous Poisson Process -- 1.1.2. Alternative Definitions of the Poisson Process -- 1.1.3. Overdispersion -- 1.1.4. Contagion -- 1.1.5. Estimation of the Poisson Process -- 1.2. The Weighted Poisson Process of Order i -- 1.2.1. Estimation of Poisson Process of Order i -- 1.3. Skellam Process: The Difference Between Two Poisson Processes
1.3.1. Estimation of the Skellam Process -- 1.4. The Time Non-homogeneous Poisson Process -- 1.4.1. Estimation of the Non-homogeneous Poisson Process -- 1.4.2. Doubly Stochastic (or Conditional) Poisson Process -- 1.5. Compound Poisson Processes (CPP) -- 1.5.1. Standard Compound Poisson Process -- 1.5.2. Distribution of the Maximum -- 1.5.3. Classical Ruin Theory -- 1.5.4. Estimation of a Compound Poisson Process Model for Fire Insurance -- 1.6. Poisson Random Fields -- 1.7. The Integral of an Homogeneous Poisson Process -- 1.8. Iterated Poisson: Composition of Two Independent Poisson Processes
1.9. Shot Noise and Hawkes Processes -- 1.9.1. The Shot Noise Process -- 1.9.2. Hawkes Processes -- II. Birth-and-death processes -- 2. Birth processes -- 2.1. The Nonlinear Case -- 2.2. The Linear Case (Yule-Furry) -- 2.3. Estimation of the Pure-birth Process -- 2.3.1. Estimators -- 3. Death Processes -- 3.1. The Nonlinear Case -- 3.2. The Linear Case -- 3.3. The Sublinear Case -- 3.4. Estimation of the Pure-death Process -- 3.4.1. Estimators -- 4. The Birth-death Process -- 4.1. The Nonlinear Case -- 4.2. The Linear Case -- 4.3. The Extinction Probability and the Riccati Equation
4.4. Galton-Watson Branching Processes -- 4.5. Estimation of the Birth-death Process -- III. Fractional Poisson Processes -- 5. Fractional Extensions of the Poisson and Birth and Death Processes -- 5.1. The Space-fractional Poisson Process: Standard Case -- 5.1.1. Properties of the Space-fractional Poisson Process -- 5.2. Generalized Space-fractional Poisson Processes -- 5.3. Another Fractional Generalization of the Poisson Process -- 5.4. The Time-fractional Poisson Process -- 5.4.1. Estimation of the Time-fractional Poisson Process -- 5.5. The Space-time Fractional Poisson Process
5.6. Fractional Birth-and-death Processes -- 5.6.1. The Fractional Pure-birth Process -- 5.6.2. The Fractional Pure-death Process -- 5.6.3. The Fractional Birth-death Processes -- Appendices -- References -- Analytic Index
Enzo Orsingher, Riccardo Cesari, and Vieri Mosco.
Includes bibliographical references and index.
Boca Raton, FL ; Abingdon, Oxon : CRC Press, 2026
Chapman & Hall/CRC financial mathematics series