A complete characterization of local martingales which are functions of Brownian motion and its maximum
We prove the max-martingale conjecture given in recent article with Marc Yor. We show that for a continuous local martingale $(N\_t:t\ge 0)$ and a function $H:R x R\_+\to R$, $H(N\_t,\sup\_{s\leq t}N\_s)$ is a local martingale if and only if there exists a locally integrable function $f$ such that $...
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Format: | Journal article |
Language: | English |
Published: |
2005
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