# Definition of dynamic Bayesian system, and its relation to HMM?

From Wikipedia

A Dynamic Bayesian Network (DBN) is a Bayesian Network which relates variables to each other over adjacent time steps. This is often called a Two-Timeslice BN because it says that at any point in time T, the value of a variable can be calculated from the internal regressors and the immediate prior value (time T-1). DBNs are common in robotics, and have shown potential for a wide range of data mining applications. For example, they have been used in speech recognition, protein sequencing, and bioinformatics. DBN have shown to produce equivalent solutions to Hidden Markov Models and Kalman Filters.

1. I was wondering if "the immediate prior value (time T-1)" means the time index in a DBN is always discrete?
2. Does "at any point in time T, the value of a variable can be calculated from the internal regressors and the immediate prior value (time T-1)" mean a DBN is a discrete-time Markov process?
3. If I understand correctly, a HMM is a discrete-time Markov process too, if ignoring the output from state at the same time. So I wonder if HMM and DBN are the same concept? But another Wikipedia article says

hidden Markov model (HMM) is a statistical Markov model in which the system being modeled is assumed to be a Markov process with unobserved (hidden) states. An HMM can be considered as the simplest dynamic Bayesian network.

and there is another quote from the first article:

DBN have shown to produce equivalent solutions to Hidden Markov Models and Kalman Filters.

Thanks!