Book:D.R. Cox/The Theory of Stochastic Processes

Subject Matter

 * Stochastic Processes

Contents

 * Preface
 * 1 Introduction
 * 1.1 Examples of stochastic processes
 * 1.2 Specification of stochastic processes
 * 1.3 Markov processes
 * Bibliographic notes and exercises


 * 2 The Random Walk
 * 2.1 Introduction
 * 2.2 The simple random walk
 * 2.3 The general one-dimensional random walk in discrete time
 * 2.4 Further topics
 * Bibliographic notes and exercises


 * 3 Markov Chains
 * 3.1 Introduction
 * 3.2 A two-state Markov chain
 * 3.3 General definitions and some examples
 * 3.4 The classification of states and the limit theorem
 * 3.5 Closed sets of states
 * 3.6 Irreducible chains and equilibrium distributions
 * 3.7 Branching processes
 * 3.8 Limiting properties of irreducible chains
 * 3.9 Absorption problems
 * 3.10 Non-negative square matrices
 * 3.11 Finite Markov chains
 * 3.12 Further topics
 * 3.13 Appendix on power series with non-negative coefficients
 * Bibliographic notes and exercises


 * 4 Markov Processes with Discrete States in Continuous Time
 * 4.1 The Poisson process
 * 4.2 Generalizations of the Poisson process
 * 4.3 Some simple processes of the birth-death type
 * 4.4 Equilibrium distributions
 * 4.5 General formulation
 * 4.6 Some miscellaneous topics
 * Bibliographic notes and exercises


 * 5 Markov Processes in Continuous Time with Continuous State Space
 * 5.1 Introduction
 * 5.2 Continuous limit of the simple random walk: the Wiener process
 * 5.3 The diffusion equations for the Wiener process
 * 5.4 First passage problems for the Wiener process
 * 5.5 Continuous limits of more general discrete processes
 * 5.6 The Kolmogorov equations
 * 5.7 Boundary conditions for homogeneous diffusion processes
 * 5.8 The Ornstein-Uhlenbeck process
 * 5.9 Transformations of the Wiener process
 * 5.10 First passage times for homogeneous diffusion processes
 * 5.11 Approximations to discrete processes by means of diffusion processes
 * 5.12 Continuous and jump transitions
 * 5.13 Processes with independent increments
 * 5.14 Multidimensional processes
 * Bibliographic notes and exercises


 * 6 Non-Markovian Processes
 * 6.1 Introduction
 * 6.2 The device of stages
 * 6.3 Supplementary variables
 * 6.4 Imbedded Markov process
 * Bibliographic notes and exercises


 * 7 Stationary Processes: Time Domain
 * 7.1 Introduction
 * 7.2 Some definitions and special processes
 * 7.3 Some general results about stationary processes
 * 7.4 Processes in continuous time
 * 7.5 Prediction theory
 * Bibliographic notes and exercises


 * 8 Stationary Processes: Frequency Domain
 * 8.1 Introduction
 * 8.2 The spectral representation
 * 8.3 Linear operations on stationary processes
 * 8.4 Derivation of the spectral representation
 * 8.5 Prediction and filtering theory
 * 8.6 Multivariate processes
 * Bibliographic notes and exercises


 * 9 Point Processes
 * 9.1 Introduction page
 * 9.2 The renewal process
 * 9.3 Renewal processes with more than one type of interval
 * 9.4 Stationary point processes
 * 9.5 Operations on point processes
 * 9.6 Real-valued processes associated with a point process
 * Bibliographic notes and exercises


 * Appendix 1 Table of exponentially distributed random quantities
 * Appendix 2 Bibliography
 * Author index
 * Subject index