Introduction

This chapter provides a brief historical overview of stochastic engineering dynamics and identifies various current computational challenges related to an increasingly complex modeling of diverse dynamical systems. Next, it discusses state-of-the-art solution techniques and their limitations and presents basic aspects of the theory of Markov processes and stochastic differential equations for completeness. Furthermore, the basic elements of a purely numerical solution scheme, also known as numerical path integration, based on a discretized version of the Chapman-Kolmogorov equation are discussed. The discussion is supported by an extensive literature review, and the chapter concludes with the outline of the book.