Let [itex]\phi(t)[/itex] be a Brownian Walk (Wiener Process), where [itex]\phi\in[0,2\pi)[/itex]. As such we work with the variable [itex]z(t)=e^{i\phi(t)}[/itex]. I would like to calculate(adsbygoogle = window.adsbygoogle || []).push({});

[itex]E(z(t)z(t+\tau))[/itex]

This is equal to [itex]E(e^{i\phi(t)+i\phi(t+\tau)})[/itex] and I know that

[itex]E(e^{i\phi(t)})=e^{-\frac{1}{2}\sigma^{2}(t)}[/itex], where the mean is 0 and [itex]\sigma^{2}(t)=2Dt[/itex].

However, I have been stuck a week on how to proceed, any thoughts?

Thank you :)

Aim For Clarity

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Autocorrelation of a wiener process

**Physics Forums | Science Articles, Homework Help, Discussion**