"Random Vibrations Theory and Applications investigates methods involved in stochastic response and stability analyses of nonlinear systems. Using a systematic approach to present the foundational framework within nonlinear systems, the book highlights the significance of effective analysis. Throughout the book, the considerable impact of selecting an appropriate method in the design and optimization of various nonlinear engineering systems is demonstrated. Exploring many methods in detail, and comparing and contrasting their individual strengths and weaknesses, the book covers the Monte Carlo simulation method, the numerical path integral solution method, the global geometric method and the first passage theory. Using case studies throughout, the book demonstrates practical applications for nonlinear engineering systems. This book would be of interest to engineers and scientists from a variety of fields, including aeronautical, civil, mechanical, and ocean engineering, who are involved in research on stochastic dynamic analysis of nonlinear systems. The book is also intended for upper undergraduate and graduate students in the field of advanced dynamic analysis technologies"--