Abstract
We propose a method to construct the stochastic integral simultaneously under a non-dominated family of probability measures. Path-by-path, and without referring to a probability measure, we construct a sequence of Lebesgue-Stieltjes integrals whose medial limit coincides with the usual stochastic integral under essentially any probability measure such that the integrator is a semimartingale. This method applies to any predictable integrand.
Citation
Marcel Nutz. "Pathwise construction of stochastic integrals." Electron. Commun. Probab. 17 1 - 7, 2012. https://doi.org/10.1214/ECP.v17-2099
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