On exponential local martingales associated with strong Markov continuous local martingales

Stefan Blei and Hans-Jürgen Engelbert

Stochastic Processes and their Applications, 2009, vol. 119, issue 9, 2859-2880

Abstract: 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.

Keywords: Continuous; local; martingales; Continuous; strong; Markov; processes; Stochastic; differential; equations; Brownian; motion; Brownian; motion; with; drift; Integral; functionals; 0-1-laws; Continuous; exponential; local; martingales; Stochastic; exponentials; Martingale; property; of; stochastic; exponentials (search for similar items in EconPapers)
Date: 2009
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (9)

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