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The Proof of Itô’s Formula: The Diagram Formula and Some of Its Consequences

  • Péter Major
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 849)

Abstract

Here we prove the most important result about multiple Wiener–Itô integrals, the so-called diagram formula together with some of its consequences. In the diagram formula we rewrite the product of Wiener–Itô integrals in the form of a sum of Wiener–Itô integrals and also give a formula (with the help of some diagrams) about the calculation the kernel-functions of the integrals appearing in this sum.

Keywords

Equivalence Class Kernel Function Spectral Measure Undirected Graph Gaussian Random Variable 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 7.
    Dobrushin, R.L.: Gaussian and their subordinated generalized fields. Ann. Probab. 7, 1–28 (1979)CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Péter Major
    • 1
  1. 1.Alfréd Rényi Mathematical Institute Hungarian Academy of SciencesBudapestHungary

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