  In order to approximate a continuous time stochastic process by discrete time
Markov chains one has several options to embed the Markov chains into
continuous time processes. On the one hand there is the Markov embedding, which
uses exponential waiting times. On the other hand each Skorokhod topology
naturally suggests a certain embedding. These are the step function embedding
for $J_1$, the linear interpolation embedding for $M_1$, the multi step
embedding for $J_2$ and a more general embedding for $M_2$. We show that the
convergence of the step function embedding in $J_1$ implies the convergence of
the other embeddings in the corresponding topologies, respectively. For the
converse statement a $J_1$-tightness condition for embedded Markov chains is
given.
  The result relies on various representations of the Skorokhod topologies.
Additionally it is shown that $J_1$ convergence is equivalent to the joint
convergence in $M_1$ and $J_2$.

Probability