  Consider a strong Markov process in continuous time, taking values in some
Polish state space. Recently, Douc, Fort and Guillin (2009) introduced
verifiable conditions in terms of a supermartingale property implying an
explicit control of modulated moments of hitting times. We show how this
control can be translated into a control of polynomial moments of abstract
regeneration times which are obtained by using the regeneration method of
Nummelin, extended to the time-continuous context.
  As a consequence, if a $p-$th moment of the regeneration times exists, we
obtain non asymptotic deviation bounds of the form
$$P_{\nu}(|\frac1t\int_0^tf(X_s)ds-\mu(f)|\geq\ge)\leq K(p)\frac1{t^{p-
1}}\frac 1{\ge^{2(p-1)}}\|f\|_\infty^{2(p-1)}, p \geq 2. $$ Here, $f$ is a
bounded function and $\mu$ is the invariant measure of the process. We give
several examples, including elliptic stochastic differential equations and
stochastic differential equations driven by a jump noise.
