Applied Probability and Stochastic Processes

PROBABILITY THEORY
RANDOM EVENTS AND THEIR PROBABILITIES
RANDOM EXPERIMENTS
RANDOM EVENTS
PROBABILITY
CONDITIONAL PROBABILITY AND INDEPENDENCE OF RANDOM EVENTS

ONE-DIMENSIONAL RANDOM VARIABLES
MOTIVATION AND TERMINOLOGY
DISCRETE RANDOM VARIABLES
CONTINUOUS RANDOM VARIABLES
MIXTURES OF RANDOM VARIABLES
GENERATING FUNCTIONS

MULTIDIMENSIONAL RANDOM VARIABLES
TWO-DIMENSIONAL RANDOM VARIABLES
n-DIMENSIONAL RANDOM VARIABLES

FUNCTIONS OF RANDOM VARIABLES
FUNCTIONS OF ONE RANDOM VARIABLE
FUNCTIONS OF SEVERAL RANDOM VARIABLES
SUMS OF RANDOM VARIABLES

INEQUALITIES AND LIMIT THEOREMS
INEQUALITIES
LIMIT THEOREMS

STOCHASTIC PROCESSES
BASICS OF STOCHASTIC PROCESSES
MOTIVATION AND TERMINOLOGY
CHARACTERISTICS AND EXAMPLES
CLASSIFICATION OF STOCHASTIC PROCESSES
TIME SERIES IN DISCRETE TIME

RANDOM POINT PROCESSES
BASIC CONCEPTS
POISSON PROCESSES
RENEWAL PROCESSES

DISCRETE-TIME MARKOV CHAINS
FOUNDATIONS AND EXAMPLES
CLASSIFICATION OF STATES
LIMIT THEOREMS AND STATIONARY DISTRIBUTION
BIRTH AND DEATH PROCESSES
DISCRETE-TIME BRANCHING PROCESSES

CONTINUOUS-TIME MARKOV CHAINS
BASIC 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

MARTINGALES
DISCRETE-TIME MARTINGALES
CONTINUOUS-TIME MARTINGALES

BROWNIAN MOTION
INTRODUCTION
PROPERTIES OF THE BROWNIAN MOTION
MULTIDIMENSIONAL AND CONDITIONAL DISTRIBUTIONS
FIRST PASSAGE TIMES
TRANSFORMATIONS OF THE BROWNIAN MOTION

SPECTRAL ANALYSIS OF STATIONARY PROCESSES
FOUNDATIONS
PROCESSES WITH DISCRETE SPECTRUM
PROCESSES WITH CONTINUOUS SPECTRUM

REFERENCES

INDEX