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I am attempting to understand Sequential Monte Carlo(SMC) deeply, but with little theoretical background on probability theory and stochastic processes. Usually, the 'statistics' perspective of markov chains and stochastics is well understood by me. But I struggle when references refer to generalized convergence theorems, measures and topological spaces. My question is what kind of mathematical background do I need to learn the book "Feynmann Kac Formulae: Genealogical and Interacting Particle Systems With Applications" by Pierre Del Moral properly? I am aiming to learn this because it is a seminal text in stochastic theory and particle models.Therefore, what learning structure of topics should I pursue to gain a deep understanding of the theories? Is there a pre-requisite book/reference that will guide me nicely into understanding the main book (such as a book that provides manageable exercises that gradually expand your knowledge as opposed to books which just offer theorems and definitions with little examples and questions)?

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    $\begingroup$ I don't know if it will "guide [you] nicely into understanding the main book" but I like this one: springer.com/us/book/9780387402642 $\endgroup$
    – Taylor
    Commented May 1, 2018 at 14:12
  • $\begingroup$ @taylor this is almost the perfect suggestion. I have had problems with measure-theoretic notation in which I refer to Erhan Cinlar's Probability and Stochastics... The hidden markov model seems to bridge between the basics of probability(in the cinlar book) with SMC. Thank you. $\endgroup$
    – tintinthong
    Commented May 2, 2018 at 5:18
  • $\begingroup$ @Taylor and also tintinthong, is the book only for countable state-spaces, or does it also explain when the state-space is $R$ or $R^d$? $\endgroup$
    – An old man in the sea.
    Commented Aug 24, 2018 at 17:26
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    $\begingroup$ @Anoldmaninthesea. it's general state space so both. Yeah, I think it's more common to say "hidden markov model" for discrete state space, but they're more general here. $\endgroup$
    – Taylor
    Commented Aug 24, 2018 at 20:23

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