# K-dimensional brownian motion

1. Jun 18, 2010

### coolnessitself

I'm trying to write a fokker planck equation for a particular SDE, but I'm caught up on an aside by the author I'm following.
He has a SDE with drift $$b \in \mathbb{R}^n$$, a dispersion matrix $$\sigma \in \mathbb{R}^{n\times k}$$, and k-dimensional brownian motion $$W_t$$, resulting in something like this
$$dX_t &=& b(X_t)dt + \sigma(X_t)dW_t$$
My confusion comes from this k-dimensional brownian motion. What is this k-th dimension? I'm guessing that X_t will take a value in n-d,and W_t is k-by-1, so that would make sigma like a covariance matrix. But what do these k components actually mean physically?

Thanks

Last edited: Jun 18, 2010