Is a Bernoulli process a Markov chain? For a Bernoulli process, the outcome of a future trial is independent of the outcome of past trials. I.e., the future behaviour of a Bernoulli process is independent of its past, i.e. a Bernoulli process posesses the Markov property. So every Bernoulli trial is a Markov chain, right?

Yes, see Breuer 2005 p. 2

References:
Breuer, L. and D. Baum (2005). An Introduction to Queueing Theory: And Matrix-Analytic Methods, Springer.
