Markov Chains pp 421-452 | Cite as

Coupling for Irreducible Kernels

  • Randal DoucEmail author
  • Eric Moulines
  • Pierre Priouret
  • Philippe Soulier
Part of the Springer Series in Operations Research and Financial Engineering book series (ORFE)


This chapter deals with coupling techniques for Markov chains. We will use these technique to obtain bounds for
$$\begin{aligned} \varDelta _n(f,\xi ,\xi ')=|\xi P^n f -\xi 'P^n f| \;, \end{aligned}$$
where f belongs to an appropriate class of functions and Open image in new window . Using the canonical space \((\mathsf {X}^\mathbb {N}, \mathscr {X}^{\otimes \mathbb {N}})\) and the notation of Chapter 3, we can write \(\varDelta _n(f,\xi ,\xi ')=|\mathbb E_\xi [f(X_n)]-\mathbb E_{\xi '}[f(X_n)]|\). In this expression, two different probability measures \(\mathbb {P}_\xi \) and \(\mathbb {P}_{\xi '}\) are used on the canonical space and the expectation of the same function \(f(X_n)\) is considered under these two probability measures.

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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Randal Douc
    • 1
    Email author
  • Eric Moulines
    • 2
  • Pierre Priouret
    • 3
  • Philippe Soulier
    • 4
  1. 1.Département CITITelecom SudParisÉvryFrance
  2. 2.Centre de Mathématiques AppliquéesEcole PloytechniquePalaiseauFrance
  3. 3.Université Pierre et Marie CurieParisFrance
  4. 4.Université Paris NanterreNanterreFrance

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