On Burkholder's supermartingales
Davis, Burgess ; Suh, Jiyeon
Illinois J. Math., Tome 50 (2006) no. 1-4, p. 313-322 / Harvested from Project Euclid
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For $0< p <\infty$, put ¶ \[ Y_t(c,p)=Y= B_t^{*(p-2)} [ B_t^2 -t ]+c B_t^{*p},\quad t>0, \] ¶ where $B_t$ is a Brownian Motion and $B_t^*=\max_{0 \leq s \leq t} |B_s|$. Then for $0< p \leq 2$, $Y$ is a submartingale if and only if $c \geq \frac{2-p}{p}$, while for $2 \leq p < \infty$, $Y$ is a supermartingale if and only if $c\leq \frac{2-p}{p}$. This extends results of Burkholder. The first of these assertions implies a strong version of some of the Burkholder-Gundy inequalities.
Publié le : 2006-05-15
Classification:  60G44,  60J65 
@article{1258059477,
     author = {Davis, Burgess and Suh, Jiyeon},
     title = {On Burkholder's supermartingales},
     journal = {Illinois J. Math.},
     volume = {50},
     number = {1-4},
     year = {2006},
     pages = { 313-322},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1258059477}
}

Davis, Burgess; Suh, Jiyeon. On Burkholder's supermartingales. Illinois J. Math., Tome 50 (2006) no. 1-4, pp.  313-322. http://gdmltest.u-ga.fr/item/1258059477/