Sentence examples for transition density is from inspiring English sources

However, the Euler-Maruyama approximation of the transition density is accurate only when is small.

We propose an importance sampling approach with an auxiliary parameter when the transition density is unknown.

The proposed procedure therefore extends the PaRIS algorithm to HMMs whose transition density is unknown and can be unbiasedly approximated.

In addition to unbiasedness, the proposed algorithm in this work requires that the estimator of the transition density is almost surely positive and upper bounded.

The main result of the article for practical applications is that the mechanism of this procedure remains valid when the transition density is approximated by a an unbiased positive estimator.

This analytical expression of the transition density is not tractable and is estimated by updating random samples at random times between t k and tk+1 using tractable proposal distributions (for instance, based on an Euler discretization of the original SDE).

This section also details the application of this algorithm when the transition density are approximated using a GPE.

Samples generated from a long run of the Markov chain using a proposal transition density are drawn from posterior distributions of interest.

In Algorithm 1, M independent copies (left (zeta ^{m}_{k-1}right)_{1le m le M}) of ζk−1 are sampled and the empirical mean of the associated estimates of the transition density are used to compute (widehat {omega }^{ell }_{k}) instead of a single realization.

The crucial and simple result (Lemma 1) of the application of the PaRIS algorithm to POD processes is that the acceptance rejection mechanism introduced in [10] ensuring the linear complexity of the procedure is still correct when the transition densities are replaced by unbiased estimates.

In this paper, sharp two-sided estimates for the transition densities of relativistic α-stable processes with mass m∈ 0,1] in C1,1 exterior open sets are established for all time t>0. These transition densities are also the Dirichlet heat kernels of m−(m2/α−Δ)α/2 with m∈ 0,1] in C1,1 exterior open sets.