| Title:
|
A sharp maximal inequality for continuous martingales and their differential subordinates (English) |
| Author:
|
Osękowski, Adam |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
63 |
| Issue:
|
4 |
| Year:
|
2013 |
| Pages:
|
1001-1018 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Assume that $X$, $Y$ are continuous-path martingales taking values in $\mathbb R^\nu $, $\nu \geq 1$, such that $Y$ is differentially subordinate to $X$. The paper contains the proof of the maximal inequality $$ \|\sup _{t\geq 0} |Y_t| \|_1\leq 2\|\sup _{t\geq 0} |X_t| \|_1. $$ The constant $2$ is shown to be the best possible, even in the one-dimensional setting of stochastic integrals with respect to a standard Brownian motion. The proof uses Burkholder's method and rests on the construction of an appropriate special function. (English) |
| Keyword:
|
martingale |
| Keyword:
|
stochastic integral |
| Keyword:
|
maximal inequality |
| Keyword:
|
differential subordination |
| MSC:
|
60G44 |
| MSC:
|
60G46 |
| idZBL:
|
Zbl 06373958 |
| idMR:
|
MR3165511 |
| DOI:
|
10.1007/s10587-013-0068-3 |
| . |
| Date available:
|
2014-01-28T14:13:17Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143613 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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