Conference

### On local martingale and its supremum: harmonic functions and beyond

Abstract:

We discuss certain facts involving a continuous local martingale $N$ and its supremum $\bar{N}$. A complete characterization of $(N,\bar{N})$-harmonic functions is proposed. This yields an important family of martingales, the usefulness of which is demonstrated, by means of examples involving the Skorokhod embedding problem, bounds on the law of the supremum, or the local time at 0, of a martingale with a fixed terminal distribution, or yet in some Brownian penalization problems. In particula...

Publication status:
Published

### Authors

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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Pages:
517-533
Publication date:
2004-12-09
DOI:
URN:
uuid:1841a912-0ce8-4cb1-b3b5-a0b1d5a1284f
Source identifiers:
188211
Local pid:
pubs:188211
ISBN:
3-540-30782-6
Keywords: