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

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


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.


Equivalence Class Kernel Function Spectral Measure Undirected Graph Gaussian Random Variable 
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    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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