  We consider the GNS Hilbert space $\mathcal{H}$ of a uniformly hyper-finite
$C^*$- algebra and study a class of unbounded Lindbladian arises from
commutators. Exploring the local structure of UHF algebra, we have shown that
the associated Hudson-Parthasarathy type quantum stochastic differential
equation admits a unitary solution. The vacuum expectation of homomorphic
co-cycle, implemented by the Hudson-Parthasarathy flow, is conservative and
gives the minimal semi-group associated with the formal Lindbladian. We also
associate conservative minimal semi-groups to another class of Lindbladian by
solving the corresponding Evan-Hudson equation.
