Pathwise Construction of Stochastic Integrals

Details Pathwise Construction of Stochastic Integrals Pathwise Construction of Stochastic Integrals

2011-08-15

arxiv.org/abs/1108.2981v1

Mathematics

Probability

8 pages

Scientific paper

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.

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