Let X be a regular linear continuous positively recurrent Markov process with state space R, scale function S and speed measure m. For a∈R denote B^+_a&=_x≥ a (]x,+∞[)(S(x)-S(a)) B^-_a&=_x≤ a (]-∞;x[)(S(a)-S(x)) We study some characteristic relations between
Nearby in the stack
Ba+
,
Ba−
, the exponential moments of the hitting times
Ta
of
X
, the Hardy and Poincaré inequalities for the Dirichlet form associated with
X
. As a corollary, we establish the equivalence between the existence of exponential moments of the hitting times and the spectral gap of the generator of