Introduction to Stochastic Process Theory and its Uses

Abstract

In the preceding chapters, loads and strengths have mainly been modelled by random variables with associated distribution functions. However, a load S on a given structure will usually be time-varying S(t). The function S(t) is stochastic (random) in the sense that the value of S at a given time t is an outcome of a random variable. In this way, by modelling the time history and the randomness of a physical quantity by an (infinite) number of random variables, a so-called stochastic process is obtained. In section 9.2 a more formal definition of this concept will be given, but it is not possible to give a detailed treatment of the theory of stochastic processes here. Only the most fundamental notions will be introduced and only one special type of stochastic processes will be described in more detail.