Stability of Feynman-Kac Semigroups
This chapter is devoted to structural and stability properties of Feynman-Kac semigroups. These regularity properties appear to be central in the understanding of various topics discussed in this book. They will be applied in Chapter 5 to analyze the existence and the uniqueness of invariant measures, and in Chapter 12 they are used to study the asymptotic stability of nonlinear filtering equations. In Chapter 6, we will also use these results to analyze the concentration properties of annealed Feynman-Kac semigroups associated with a cooling schedule. Their applications to the study of the long time behavior of particle methods will be the main object of Chapter 7.
KeywordsRelative Entropy Regularity Property Contraction Property Functional Inequality Markov Semigroup
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