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On the Original Wiener–Itô Integral

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Part of the Lecture Notes in Mathematics book series (LNM,volume 849)

Abstract

Here we discuss the original Wiener–Itô integrals with respect to a random orthogonal measure. We give their most important properties and also present some results about their relation to the Wiener–Itô integrals with respect to a random spectral measure and to the classical Itô integrals of stochastic processes.

Keywords

  • White Noise
  • Lebesgue Measure
  • Measure Space
  • Simple Function
  • Unitary Transformation

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References

  1. Itô, K.: Multiple Wiener integral. J. Math. Soc. Jpn. 3, 157–164 (1951)

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© 2014 Springer International Publishing Switzerland

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Major, P. (2014). On the Original Wiener–Itô Integral. In: Multiple Wiener-Itô Integrals. Lecture Notes in Mathematics, vol 849. Springer, Cham. https://doi.org/10.1007/978-3-319-02642-8_7

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