Introduction

The last decade has seen a dramatic increase in the use of Monte Carlo methodsfor solving stochastic engineering problems. There are primarily two reasons forthis increase. First, the computational power available today, even for a laptopcomputer, is formidable and steadily increasing. Second, the versatility ofMonte Carlo methods make them very attractive as a way of obtaining solutions tostochastic problems. The drawback of Monte Carlo methods for a range of problemshas been that the required numerical calculations may take days, weeks or evenmonths to do. But this situation is changing, some numerical problems thatrequired several days of computer time for their solution just a few years agocan now be solved in minutes or hours. This has really opened the door for theuse of Monte Carlo-based methods for solving a wide array of stochasticengineering problems. In this chapter the focus is on adapting Monte Carlomethods for estimation of extreme values of stochastic processes encountered invarious engineering disciplines.

Simulation of Stationary Stochastic Processes

The approach to the simulation of stationary stochastic processes favored in thisbook is the spectral representation method. The main reason for this is itssimplicity and transparency for practical applications. This choice has, infact, already been implemented at several places previously in this book. Takentogether, they constitute a fairly complete description on the level needed hereof how to simulate a stationary process.