PROBABILITY AND ITS APPLICATIONS
CONTENTS EARLY HISTORY 11 LIFE TABLES AND RENEWAL THEORY 12 COUNTING PROBLEMS 13 SOME MORE RECENT DEVELOPMENTS BASIC PROPERTIES OF THE POISSON PROCESS 21 THE STATIONARY POISSON PROCESS 22 CHARACTERIZATIONS OF THE STATIONARY POISSON PROCESS: I COMPLETE RANDOMNESS 23 CHARACTERIZATIONS OF THE STATIONARY POISSON PROCESS: II THE FORM OF THE DISTRIBUTION 24 THE GENERAL POISSON PROCESS SIMPLE RESULTS FOR STATIONARY POINT PROCESSES ON THE LINE 31 SPECI?CATION OF A POINT PROCESS ON THE LINE 32 STATIONARITY: DE?NITIONS 33 MEAN DENSITY, INTENSITY, AND BATCH-SIZE DISTRIBUTION 34 PALM–KHINCHIN EQUATIONS 35 ERGODICITY AND AN ELEMENTARY RENEWAL THEOREM ANALOGUE 36 SUBADDITIVE AND SUPERADDITIVE FUNCTIONS RENEWAL PROCESSES 41 BASIC PROPERTIES 42 STATIONARITY AND RECURRENCE TIMES 43 OPERATIONS AND CHARACTERIZATIONS 44 RENEWAL THEOREMS 45 NEIGHBOURS OF THE RENEWAL PROCESS: WOLD PROCESSES 46 STIELTJES-INTEGRAL CALCULUS AND HAZARD MEASURES FINITE POINT PROCESSES 51 AN ELEMENTARY EXAMPLE: INDEPENDENTLY AND IDENTICALLY DISTRIBUTED CLUSTERS 52 FACTORIAL MOMENTS, CUMULANTS, AND GENERATING FUNCTION RELATIONS FOR DISCRETE DISTRIBUTIONS 53 THE GENERAL FINITE POINT PROCESS: DE?NITIONS AND DISTRIBUTIONS 54 MOMENT MEASURES AND PRODUCT DENSITIES 55 GENERATING FUNCTIONALS AND THEIR EXPANSIONS MODELS CONSTRUCTED VIA CONDITIONING: COX, CLUSTER, AND MARKED POINT PROCESSES 61 IN?NITE POINT FAMILIES AND RANDOM MEASURES 62 COX (DOUBLY STOCHASTIC POISSON) PROCESSES 63 CLUSTER PROCESSES 64 MARKED POINT PROCESSES CONDITIONAL INTENSITIES AND LIKELIHOODS 71 LIKELIHOODS AND JANOSSY DENSITIES 72 CONDITIONAL INTENSITIES, LIKELIHOODS, AND COMPENSATORS 73 CONDITIONAL INTENSITIES FOR MARKED POINT PROCESSES 74 RANDOM TIME CHANGE AND A GOODNESS-OF-FIT TEST 75 SIMULATION AND PREDICTION ALGORITHMS 76 INFORMATION GAIN AND PROBABILITY FORECASTS SECOND-ORDER PROPERTIES OF STATIONARY POINT PROCESSES 81 SECOND-MOMENT AND COVARIANCE MEASURES 82 THE BARTLETT SPECTRUM 83 MULTIVARIATE AND MARKED POINT PROCESSES 84 SPECTRAL REPRESENTATION 85 LINEAR FILTERS AND PREDICTION 86 PPD MEASURES