This book presents broadly applicable methods for the large deviation and moderate deviation analysis of discrete and continuous time stochastic systems. A feature of the book is the systematic use of variational representations for quantities of interest such as normalized logarithms of probabilities and expected values. By characterizing a large deviation principle in terms of Laplace asymptotics, one converts the proof of large deviation limits into the convergence of variational representations. These features are illustrated though their application to a broad range of discrete and continuous time models, including stochastic partial differential equations, processes with discontinuous statistics, occupancy models, and many others. The tools used in the large deviation analysis also turn out to be useful in understanding Monte Carlo schemes for the numerical approximation of the same probabilities and expected values. This connection is illustrated through the design and analysis of importance sampling and splitting schemes for rare event estimation. The book assumes a solid background in weak convergence of probability measures and stochastic analysis, and is suitable for advanced graduate students, postdocs and researchers.

From a young backpacker, sleeping on a park bench in Japan, to becoming a senior leader of one of the biggest corporate giants in the world, Paul Dupuis has built a career through game-changing leadership - crafted through his own real-life experiences as an athlete, volunteer and CEO. The E5 is both familiar and fresh. It's a leadership model built in the spirit of 'standing on the shoulders of giants', learning from leaders like Konosuke Matsushita, the founder of Panasonic who put 'empathy' and 'enable' at the core of his leadership approach. And Jack Welch with his 3E's, who then inspired Bob McDonald at P&G to craft his own version of the 5E's, to Jim Collins who shared his version of Level 5 Leadership in the book, 'Good to Great', with execution at the core. The E5 Movement is a call to action to all leaders, globally, to lead with impact. The five Es are: envision; express; excite; enable; execute. These five rules of leadership are both timeless and borderless. The real-life anecdotes, combined with the conversational tone of the book, make this an accessible and impactful read. Thought-provoking and practical, this book will inspire leaders to think about their own leadership, adopting the five Es on their mission to lead their teams to excellence - a true game changer. Pick your five and join the movement!

This book presents broadly applicable methods for the large deviation and moderate deviation analysis of discrete and continuous time stochastic systems. A feature of the book is the systematic use of variational representations for quantities of interest such as normalized logarithms of probabilities and expected values. By characterizing a large deviation principle in terms of Laplace asymptotics, one converts the proof of large deviation limits into the convergence of variational representations. These features are illustrated though their application to a broad range of discrete and continuous time models, including stochastic partial differential equations, processes with discontinuous statistics, occupancy models, and many others. The tools used in the large deviation analysis also turn out to be useful in understanding Monte Carlo schemes for the numerical approximation of the same probabilities and expected values. This connection is illustrated through the design and analysis of importance sampling and splitting schemes for rare event estimation. The book assumes a solid background in weak convergence of probability measures and stochastic analysis, and is suitable for advanced graduate students, postdocs and researchers.