TABLE OF CONTENTS The random response of dynamic systems is usually given in the form of a time history record. Each record is called a realization or a sample function. The collection of all possible records (sample functions) is called the ensemble or the random process [1; 2]. Figure 8.1 portrays a typical example of the realizations of a random process, X( t), where t is the parameter, say, time. The superscript j = 1,2, in x j( t) represents the jth realization of the random process X( t). At fixed times t = t 1 and t 2, X( t 1) and X( t 2) are random variables, and X j( t 1) and X j( t 2) are their jth realizations.
A random process, X( ?, t), which in the literature is also called a random function, a stochastic process, or a time series if the index parameter t is time, is defined as a parametered family of random variables with two parameters (arguments) ? ? ? denoting that ? belongs to the parent set ?, and t ? T denoting that t belongs to the parent set T, where ?
