  The paper deals with the two-state (opening-closing of base pairs) model used
to describe the fluctuation dynamics of a single bubble formation. We present
an exact solution for the discrete and finite size version of the model that
includes end effects and derive analytic expressions of the correlation
function, survival probability and lifetimes for the bubble relaxation
dynamics. It is shown that the continuous and semi-infinite limit of the model
becomes a good approximation to exact result when a^N << 1, where N is bubble
size and a, the ratio of opening to closing rates of base pairs, is the control
parameter of DNA melting.
