On pathwise rate conservation for a class of semi-martingales

Ravi Mazumdar, Vivek Badrinath, Fabrice Guillemin and Catherine Rosenberg

Stochastic Processes and their Applications, 1993, vol. 47, issue 1, 119-130

Abstract: In this paper, we generalize an earlier result on pathwise rate conservation for càdlàg processes to include a diffusion component. This leads to the occurence of an additional term corresponding to the local time of the process when considering the level crossing formula. This extension serves to show that rate conservation is a pathwise property of a càdlàg process subject to it satisfying an o(t) growth condition almost surely. When specialized to the stationary case, we obtain a characterization of the invariant distribution of semi-martingales. We then illustrate the application of the conservation law to obtain the invariant distribution of a reflected Ornstein-Uhlenbeck process.

Keywords: rate; conservation; martingales; nonstationary; local; time; Palm; probabilities; queues (search for similar items in EconPapers)
Date: 1993
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