Local times and almost sure convergence of semi-martingales (Q1901158)
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scientific article; zbMATH DE number 812596
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Local times and almost sure convergence of semi-martingales |
scientific article; zbMATH DE number 812596 |
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Local times and almost sure convergence of semi-martingales (English)
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1 April 1996
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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.
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Brownian motion
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semi-martingales
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asymptotic behaviour
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local times
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