  This paper focuses on Sequential Monte Carlo approximations of smoothing
distributions in conditionally linear and Gaussian state spaces. To reduce
Monte Carlo variance of smoothers, it is typical in these models to use
Rao-Blackwellization: particle approximation is used to sample sequences of
hidden regimes while the Gaussian states are explicitly integrated conditional
on the sequence of regimes and observations, using variants of the Kalman
filter / smoother. The first successful attempt to use Rao-Blackwellization for
smoothing extends the Bryson-Frazier smoother for Gaussian linear state space
models using the generalized two-filter formula together with Kalman filters /
smoothers. More recently, a forward backward decomposition of smoothing
distributions mimicking the Rauch-Tung-Striebel smoother for the regimes
combined with backward Kalman updates has been introduced. This paper
investigates the benefit of introducing additional rejuvenation steps in all
these algorithms to sample at each time instant new regimes conditional on the
forward and backward particles. This defines particle based approximations of
the smoothing distributions whose support is not restricted to the set of
particles sampled in the forward or backward filter. These procedures are
applied to commodity markets which are described using a two factor model based
on the spot price and a convenience yield for crude oil data.
