Negatively Correlated Diffusive Processes I am trying to generate 2 diffusive process that are correlated. 
One way that was recommended was to set up the process such that the changes are correlated - both processes have 0 drift and correlated noise acting on both the processes. 
More concretely, define the random increments of both processes as 
$\delta X = \xi \sqrt{1+\rho} + \hat{\xi}\sqrt{1-\rho} \\\delta Y = \xi \sqrt{1+\rho} - \hat{\xi}\sqrt{1-\rho} $.
where $\xi, \hat{\xi}$ are independent noise term with zero mean and equal arbitrary variance. $\rho$ is the correlation coefficient of the increments between both processes.
I am having trouble proving (and understanding the intuition) why this definition of increments would generate a correlated process. 
I am aware that a Brownian motion defined as $Z(t) = \rho B(t) + \sqrt{1-\rho^2}B^*(t)$ $(B(t), B^*(t) \text{ are independent Brownian process})$ will be correlated to B(t) with correlation coefficient of $\rho$. But this of very little help to show that $\delta X, \delta Y$ are correlated.
Thank you in advance for any help.

Hint:
$$E(\,\delta X\delta Y\,) = E(\,\xi^2 (1+\rho)-   \hat{\xi}^2 (1-\rho)\,)= E(\,\xi^2) (1+\rho)-   E(\hat{\xi}^2) (1-\rho),$$
and $$E(\,\xi^2\,)  =E(\hat{\xi}^2)  $$ 
