Maximal Inequalities for Martingales and Their Differential Subordinates

Adam Ose¸kowski ()
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Adam Ose¸kowski: University of Warsaw

Journal of Theoretical Probability, 2014, vol. 27, issue 1, 1-21

Abstract: Abstract 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 $$\beta =2.585\ldots $$ is the best possible.

Keywords: Martingale; Maximal inequality; Differential subordination; Primary 60G44; Secondary 60G42 (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s10959-012-0458-8

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