Point Processes  book cover
1st Edition

Point Processes




ISBN 9780412219108
Published July 17, 1980 by Chapman & Hall
188 Pages

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Book Description

This book describes the properties of stochastic probabilistic models and develops the applied mathematics of stochastic point processes. It is useful to students and research workers in probability and statistics and also to research workers wishing to apply stochastic point processes.

Table of Contents

Preface

1 Introduction

    1. Preliminary remarks
    2. Four illustrative examples

  1. Poisson processes
  2. Renewal processes
  3. Linear self-exciting processes
  4. Doubly stochastic Poisson processes

    1. The specification and properties of point processes
    2. Some generalizations

  1. Multiple occurrences
  2. Multivariate processes
  3. Marked processes
  4. Spatial and multidimensional processes
  5. Discrete time processes

Bibliographic notes, 1

Further results and exercises, 1

  1. Theoretical framework
    1. Some basic definitions
    2. Stationarity
    3. Orderliness
    4. Palm distributions
    5. Moments
    6. Spectral properties
    7. The probability generating functional
    8. Multivariate and multidimensional processes

    Bibliographic notes, 2

    Further results and exercises, 2

  2. Special Models
    1. Poisson processes

  1. Introduction
  2. Non-stationary Poisson processes
  3. Compound Poisson processes
  4. Cluster processes
  5. Doubly stochastic Poisson processes

    1. Renewal processes and generalizations

  1. Introduction
  2. Semi-Markov processes
  3. Moran’s process with pairwise dependent intervals
  4. Processes with Markov-depended intervals
  5. Autoregressive and moving average processes
  6. A process with independent locations

    1. Simple intensity-based models

  1. Introduction
  2. Linear self-exciting processes
  3. Doubly stochastic Poisson processes

    1. Cluster processes
    2. Processes of bounded variability
    3. Level crossings
    4. Concluding remarks

Bibliographic notes

Further results and exercises

  1. Operations on point processes
    1. Preliminary remarks
    2. Operational time
    3. Thinning
    4. Translation
    5. Superposition
    6. Infinite divisibility

    Bibliographic notes

    Further results and exercises

  2. Multivariate point processes
    1. Preliminary remarks
    2. Some general concepts

  1. Definitions
  2. Specification of processes
  3. Conditional intensity functions

    1. Some special processes

  1. Notions of independence
  2. Doubly stochastic, cluster and linear self-exciting processes
  3. Processes based on recurrence times
  4. Processes produced by random displacements

    1. An application to electronic counters
    2. Marked point processes
    3. More complex marked processes

  1. Introduction
  2. Simple shot noise
  3. Marks of random extent
  4. Some general second-order results

Bibliographic notes

Further results and exercises

  1. Spatial processes
    1. Preliminary remarks
    2. Some simple generalizations of one-dimensional processes

  1. Poisson processes
  2. Doubly stochastic Poisson processes
  3. Poisson cluster processes
  4. A process with independent locations
  5. Renewal processes

    1. Some special constructions in two dimensions

  1. Constructions using concentric circles
  2. A markov construction
  3. Lattice-based processes

    1. Spatial-temporal processes

  1. Introduction
  2. Processes of points in space-time
  3. Non-interacting Poisson processes with birth, death and movement
  4. Processes with immigration
  5. Systems with interaction

Bibliographic notes

Further results and exercises

References

Author index

Subject index

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