A non-linear Riesz respresentation in probabilistic potential theory
Please always quote using this URN:urn:nbn:de:0296-matheon-2578
- For a nice Markov process such as Brownian motion on a bounded domain, we introduce a non-linear potential operator defined in terms of running suprema, and we prove a non-linear Riesz representation of a given function as the sum of a harmonic function and a non-linear potential. The proof involves a family of optimal stopping problems in analogy to the general construction of Bank and El Karoui [3], but here the analysis is carried out in terms of probabilistic potential theory.
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| Author: | Nicole El Karoui, Hans Föllmer |
|---|---|
| URN: | urn:nbn:de:0296-matheon-2578 |
| Referee: | Hans Föllmer |
| Document Type: | Preprint, Research Center Matheon |
| Language: | English |
| Date of first Publication: | 2005/05/17 |
| Release Date: | 2005/05/17 |
| Preprint Number: | 251 |
