A generalisation of the Burkholder-Davis-Gundy inequalities
| Autor: | Jacka, Saul, Hérnandez-Hérnandez, Ma. Elena |
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| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | Electron. Commun. Probab. 27: 1-8 (2022) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1214/22-ECP493 |
| Popis: | {Consider a c\`adl\`ag local martingale $M$ with square brackets $[M]$. In this paper, we provide upper and lower bounds for expectations of the type ${\mathbb E} [M]^{q/2}_{\tau}$, for any stopping time $\tau$ and $q\ge 2$, in terms of predictable processes. This result can be thought of as a Burkholder-Davis-Gundy type inequality in the sense that it can be used to relate the expectation of the running maximum $|M^*|^q$ to the expectation of the dual previsible projections of the relevant powers of the associated jumps of $M$. The case for a class of moderate functions is also discussed. Comment: 8 pages |
| Databáze: | arXiv |
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