Читать книгу Gauge Integral Structures for Stochastic Calculus and Quantum Electrodynamics - Patrick Muldowney - Страница 28

1 ¹ In fact is a finite family so there are only finitely many cases to check for additivity.

2 ² [MTRV] also deals with complex‐valued random variables. Also, in the classical definition of the Itô integral (I1, I2, I3, I4 above) the integrands are measurable functions whose values are random variables (so the values are functions rather than numbers).

3 ³ A Stieltjes integral is “the integral of a point function with respect to a point function ”, . See section 1.4 of [MTRV], pages 7–14.

4 ⁴ In accordance with the presentation in [MTRV], notation (square brackets) is used with random variables (conceived “naively” or “realistically” as potential data, along with their probabilities), while round brackets are used when random variables are interpreted as ‐measurable functions .

5 ⁵ R. Feynman proposed something on those lines to deal with an analogous problem in the path integral theory of quantum mechanics. See his comments on “subdivision and limiting processes” quoted in page 17 above.