Applied Probability and Stochastic Processes, Second Edition

Description

PROBABILITY THEORYRANDOM EVENTS AND THEIR PROBABILITIESRANDOM EXPERIMENTS RANDOM EVENTS PROBABILITY CONDITIONAL PROBABILITY AND INDEPENDENCE OF RANDOM EVENTS ONE-DIMENSIONAL RANDOM VARIABLESMOTIVATION AND TERMINOLOGY DISCRETE RANDOM VARIABLES CONTINUOUS RANDOM VARIABLES MIXTURES OF RANDOM VARIABLES GENERATING FUNCTIONS MULTIDIMENSIONAL RANDOM VARIABLESTWO-DIMENSIONAL RANDOM VARIABLES n-DIMENSIONAL RANDOM VARIABLES FUNCTIONS OF RANDOM VARIABLESFUNCTIONS OF ONE RANDOM VARIABLE FUNCTIONS OF SEVERAL RANDOM VARIABLES SUMS OF RANDOM VARIABLES INEQUALITIES AND LIMIT THEOREMSINEQUALITIES LIMIT THEOREMS STOCHASTIC PROCESSESBASICS OF STOCHASTIC PROCESSESMOTIVATION AND TERMINOLOGY CHARACTERISTICS AND EXAMPLES CLASSIFICATION OF STOCHASTIC PROCESSES TIME SERIES IN DISCRETE TIME RANDOM POINT PROCESSESBASIC CONCEPTS POISSON PROCESSES RENEWAL PROCESSES DISCRETE-TIME MARKOV CHAINSFOUNDATIONS AND EXAMPLES CLASSIFICATION OF STATES LIMIT THEOREMS AND STATIONARY DISTRIBUTION BIRTH AND DEATH PROCESSES DISCRETE-TIME BRANCHING PROCESSES CONTINUOUS-TIME MARKOV CHAINSBASIC CONCEPTS AND EXAMPLES TRANSITION PROBABILITIES AND RATES STATIONARY STATE PROBABILITIES SOJOURN TIMES IN PROCESS STATES CONSTRUCTION OF MARKOV SYSTEMS BIRTH AND DEATH PROCESSES APPLICATIONS TO QUEUEING MODELS SEMI-MARKOV CHAINS MARTINGALESDISCRETE-TIME MARTINGALES CONTINUOUS-TIME MARTINGALES BROWNIAN MOTIONINTRODUCTION PROPERTIES OF THE BROWNIAN MOTION MULTIDIMENSIONAL AND CONDITIONAL DISTRIBUTIONS FIRST PASSAGE TIMESTRANSFORMATIONS OF THE BROWNIAN MOTION SPECTRAL ANALYSIS OF STATIONARY PROCESSESFOUNDATIONS PROCESSES WITH DISCRETE SPECTRUM PROCESSES WITH CONTINUOUS SPECTRUM REFERENCES INDEX Exercises appear at the end of each chapter.