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Zbl 0834.60047
Rajeev, B.; Yor, M.
Local times and almost sure convergence of semi-martingales. (English)
[J] Ann. Inst. Henri Poincaré, Probab. Stat. 31, No.4, 653-667 (1995). ISSN 0246-0203

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.
[A.Gut (Uppsala)]

MSC 2000:: *60G48 Generalizations of martingales
60J55 Additive functionals

Keywords: Brownian motion; semi-martingales; asymptotic behaviour; local times

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