Rajeev, B.; Yor, M. Local times and almost sure convergence of semi-martingales. (English) Zbl 0834.60047 Ann. Inst. Henri Poincaré, Probab. Stat. 31, No. 4, 653-667 (1995). If \(h(t)\) is a nonnegative function, \(\{B(t)\}\) a Brownian motion and if \(h(t) B(t)\) converges as \(t \to \infty\), then it must converge to 0, because the set \(\{t : B(t) = 0\}\) is unbounded. Motivated by this example the authors investigate the connection between a.s. convergence of semi-martingales and the asymptotic behaviour of their local times. Reviewer: A.Gut (Uppsala) MSC: 60G48 Generalizations of martingales 60J55 Local time and additive functionals Keywords:Brownian motion; semi-martingales; asymptotic behaviour; local times PDFBibTeX XMLCite \textit{B. Rajeev} and \textit{M. Yor}, Ann. Inst. Henri Poincaré, Probab. Stat. 31, No. 4, 653--667 (1995; Zbl 0834.60047) Full Text: Numdam EuDML