On exponential local martingales associated with strong Markov continuous local martingales

We investigate integral functionals , t>=0, where m is a nonnegative measure on and LY is the local time of a Wiener process with drift, i.e., Yt=Wt+t, t>=0, with a standard Wiener process W. We give conditions for a.s. convergence and divergence of Tt, t>=0, and T[infinity]. In the second part of the present note we apply these results to exponential local martingales associated with strong Markov continuous local martingales. In terms of the speed measure of a strong Markov continuous local martingale, we state a necessary and sufficient condition for the exponential local martingale associated with a strong Markov continuous local martingale to be a martingale.