This rather long chapter focuses on the applications of Feynman-Kac modeling strategies and their interacting particle interpretations to a variety of practical problems. The field of applications includes spectral analysis of Feynman-Kac and Schrödinger semigroups, rare event estimation, sequential analysis of probability ratio tests, Dirichlet problems with boundary conditions, directed polymer simulations, and nonlinear filtering problems. As an initiated reader will immediately notice, all these problems consist of solving a more or less complex Feynman-Kac distribution. At the risk of repetition, we have chosen to include this chapter because we felt that there is no textbook or journal article that really illustrates the potential applications of Feynman-Kac and particle models. In the opposite situation, a reader not initiated on Feynman-Kac and particle models is recommended to read Chapter 11 before entering into the former exposition. Chapter 11 leaves out theoretical issues and it guides the reader through most of the important concepts and techniques needed in applications. For a more thorough training on Feynman-Kac and particle models, it is convenient to read Chapters 2 and 3.
KeywordsMarkov Chain Potential Function Lyapunov Exponent Particle Model Simple Random Walk
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