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Search: authors:"Adam Ose¸kowski"

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Maximal Inequalities for Martingales and Their Differential Subordinates

We introduce a method of proving maximal inequalities for Hilbert- space-valued differentially subordinate local martingales. As an application, we prove that if \(X=(X_t)_{t\ge 0},\, Y=(Y_t)_{t\ge 0}\) are local martingales such that \(Y\) is differentially subordinate to \(X\), then $$\begin{aligned} ||Y||_1\le \beta ||\sup _{t\ge 0}|X_t|\;||_1, \end{aligned}$$where \(\beta ...