Monte Carlo Methods and Extreme Value Estimation

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