This research monograph deals with fast stochastic simulation based on
im- portance sampling (IS) principles and some of its applications. It
is in large part devoted to an adaptive form of IS that has proved to be
effective in appli- cations that involve the estimation of probabilities
of rare events. Rare events are often encountered in scientific and
engineering processes. Their charac- terization is especially important
as their occurrence can have catastrophic consequences of varying
proportions. Examples range from fracture due to material fatigue in
engineering structures to exceedance of dangerous levels during river
water floods to false target declarations in radar systems. Fast
simulation using IS is essentially a forced Monte Carlo procedure
designed to hasten the occurrence of rare events. Development of this
simu- lation method of analysis of scientific phenomena is usually
attributed to the mathematician von Neumann, and others. Since its
inception, MC simula- tion has found a wide range of employment, from
statistical thermodynamics in disordered systems to the analysis and
design of engineering structures characterized by high complexity.
Indeed, whenever an engineering problem is analytically intractable
(which is often the case) and a solution by nu- merical techniques
prohibitively expensive computationally, a last resort to determine the
input-output characteristics of, or states within, a system is to carry
out a simulation.
