  In the hidden Markov process, there is a possibility that two different
transition matrices for hidden and observed variables yield the same stochastic
behavior for the observed variables. Since such two transition matrices cannot
be distinguished, we need to identify them and consider that they are
equivalent, in practice. We address the equivalence problem of hidden Markov
process in a local neighborhood by using the geometrical structure of hidden
Markov process. For this aim, we introduce a mathematical concept to express
Markov process, and formulate its exponential family by using generators. Then,
the above equivalence problem is formulated as the equivalence problem of
generators. Taking this equivalence problem into account, we derive several
concrete parametrizations in several natural cases.
