Abstract
The paper combines two objects rather different at first glance: spaces of stochastic processes having weighted bounded mean oscillation (weighted BMO) and the approximation of certain stochastic integrals, driven by the geometric Brownian motion, by integrals over piece-wise constant integrands. The consideration of the approximation error with respect to weighted BMO implies Lp and uniform distributional estimates for the approximation error by a John-Nirenberg type theorem. The general results about weighted BMO are given in the first part of the paper and applied to our approximation problem in the second one.
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