Assume A10.13 and that ϑs ≡ 1 for all t ∈ {1,...,n} and Q T ≡ M. Show that In this exercise, we provide an alternate proof of the central limit theorem for the auxiliary particle filter, based on the...

Assume A10.13 and that ϑs ≡ 1 for all t ∈ {1,...,n} and Q_T
≡ M. Show that

In this exercise, we provide an alternate proof of the central limit theorem for the auxiliary particle filter, based on the decomposition (10.58). This proof allows us to obtain an explicit expression of the asymptotic variance. Assume A10.13. Set for