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Local times and almost sure convergence of semi-martingales. (English) Zbl 0834.60047

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
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