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Burkholder’s function and a weighted \(L^2\) bound for stochastic integrals. (English) Zbl 07243366
Summary: Let \(X\) be a continuous-path martingale and let \(Y\) be a stochastic integral, with respect to \(X\), of some predictable process with values in \([-1,1]\). We provide an explicit formula for Burkholder’s function associated with the weighted \(L^2\) bound \[ \Vert Y\Vert_{L^2(W)}\lesssim [w]_{A_2}\Vert X\Vert_{L^2(W)}. \]
MSC:
60G42 Martingales with discrete parameter
60G44 Martingales with continuous parameter
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