square root processes with correlated deriving Brownian motion - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-20T07:04:32Z http://mathoverflow.net/feeds/question/53054 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/53054/square-root-processes-with-correlated-deriving-brownian-motion square root processes with correlated deriving Brownian motion startover 2011-01-24T13:18:41Z 2011-02-23T10:22:17Z <p>$$dX = \kappa_x (\theta_x - X)dt + \sigma_x \sqrt{X} \,dW_x$$ $$dY = \kappa_y (\theta_y - Y)dt + \sigma_y \sqrt{Y} \,dW_y$$ $$dW_x dW_y = \rho\, dt$$</p> <p>we know that $X$ and $Y$ are marginally distributed as non-central $\chi^2$. What is the joint distribution of $X$ and $Y$ ?</p> http://mathoverflow.net/questions/53054/square-root-processes-with-correlated-deriving-brownian-motion/53341#53341 Answer by The Bridge for square root processes with correlated deriving Brownian motion The Bridge 2011-01-26T10:20:13Z 2011-01-26T10:20:13Z <p>Hi,</p> <p>So what you really want to know can be put into this form : </p> <p>Does there exists a multivariate extension to $\chi^2$ laws, and if so, does it matches the joint law of the bivariate process $(X,Y)$. Is that right ?</p> <p>I think that you should have a look at Whishart processes and distributions </p> <p>Regards</p>