A sharp maximal inequality for continuous martingales and their differential subordinates

Title:

A sharp maximal inequality for continuous martingales and their differential subordinates

Creator:

Osekowski, Adam

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:75b673e8-655a-445e-ad67-1878db60eb5a
uuid:75b673e8-655a-445e-ad67-1878db60eb5a

Subject:

martingale, stochastic integral, maximal inequality, and differential subordination

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

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.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

1001-1018

Source:

Czechoslovak Mathematical Journal | 2013 Volume:63 | Number:4

Harvested from:

CDK

Metadata only:

false