3
$\begingroup$

Assume that we have $\epsilon_1, \; \epsilon_2$ independent white noises.

  1. Can I write $\int_{0}^1 \epsilon_1^2(t)dt$

  2. Can I write $\int_{0}^1 \epsilon_1(t) \epsilon_2(t)dt$

1 and 2 obviously make no sense in $L^2$ nor in terms of Wiener integral. Is there any way I can make sense out of it?

$\endgroup$
1
  • $\begingroup$ The answer provided by Carlo Beenakker was very helpful. However the articles provided do not cover the case of white noise multiplication - only powers. Does anyone have any clue? $\endgroup$ Oct 18, 2016 at 4:10

1 Answer 1

3
$\begingroup$

A consistent framework for "nonlinear stochastic calculus" has been developed in The square of white noise as a Jacobi field (2004), building on earlier work in Squared white noise and other non-Gaussian noises as Lévy processes on real Lie algebras (2002). A more pedestrian approach (perhaps more suited to your purpose) is taken in On powers of Gaussian white noise (2010), and Spectra for the product of Gaussian noises (2012).

$\endgroup$
1
  • $\begingroup$ Is there a place to read an introductory and simple information White Noise? Specifically about its Auto Correlation Function? $\endgroup$
    – Royi
    Jun 16, 2018 at 19:31

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.