2
votes
1answer
79 views

Expectation of product of correlated Brownian motions at different time points

Given the information about the correlation of two Brownian motions as $E[dW_1 dW_2] = \rho dt$ and knowing that $E[W_1(t)W_1(t')] = \min(t,t')$, I want to compute $E[W_1(t)W_2(t')]$ I interpret ...
1
vote
1answer
664 views

Correlation coefficient of Wiener process

First, I'm not majoring mathematics. I'm studying economics and during reading a thesis I can't understand the 'wiener process' well. I read some books about it and understand the main idea and ...
0
votes
0answers
84 views

Correlation function of Brownian motion. What am I doing wrong?

Can anyone tell me where I am going wrong here? (I am leaving out any random fluctuation forcings, because I don't think they are relevant to my problem.) 1: $\displaystyle \frac{dv(t)}{dt}=-\eta ...
3
votes
1answer
131 views

Autocorrelation of wrapped Wiener process

Let $\phi(t)$ be a Brownian Walk (Wiener Process), where $\phi\in[0,2\pi)$. As such we work with the variable $z(t)=e^{i\phi(t)}$. I would like to calculate $$E(z(t)z(t+\tau)).$$ This is equal to ...
2
votes
0answers
161 views

Correlated diffusion processes and covariance matrix

I'm really noob in maths topics so I hope you will excuse me if I use terms which aren't correct. I would like to simulate $n$ dimensional diffusion processes with $n$ noises. Each process has its ...