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Brownian Motion, 2nd Edition by Björn Böttcher, Lothar Partzsch, René L. Schilling

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15 Stochastic integrals: L2-Theory

A function ƒ : [0, T] → e9783110307290_i3215.jpg is Riemann integrable if the Riemann sums

e9783110307290_i3216.jpg

(15.1)

converge to a finite limit I. The limit is taken along all finite partitions of the interval e9783110307290_i3217.jpg, with e9783110307290_i3218.jpgand it is independent of the particular sequence and the choice of the intermediate points . The number I is called the definite Riemann integral ...

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