## Electronic Communications in Probability

### Pathwise construction of stochastic integrals

Marcel Nutz

#### 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.

#### Article information

Source
Electron. Commun. Probab., Volume 17 (2012), paper no. 24, 7 pp.

Dates
Accepted: 19 June 2012
First available in Project Euclid: 7 June 2016

https://projecteuclid.org/euclid.ecp/1465263157

Digital Object Identifier
doi:10.1214/ECP.v17-2099

Mathematical Reviews number (MathSciNet)
MR2950190

Zentralblatt MATH identifier
1245.60054

Subjects
Primary: 60H05: Stochastic integrals

Rights

#### Citation

Nutz, Marcel. Pathwise construction of stochastic integrals. Electron. Commun. Probab. 17 (2012), paper no. 24, 7 pp. doi:10.1214/ECP.v17-2099. https://projecteuclid.org/euclid.ecp/1465263157

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