Not agreed at all. I didn't insist that Ebal post his 'trivial' solution, but it follows from the well-known OU solution as given, say at wikipedia:This is closed-form because, given the driving Brownian motion B(t), it explicitly contructs "a solution" X(t) as a functional of time and B(t).With that definition of closed-form, nobody has shown any other one, so far. (Technically, there are an infinity of solutionssince the origin is regular here, but they all agree with the one shown up to the first hitting time of 0)Now, it's true that, for integer d=1,2,3,... you could drive d independent OU processes by running d independent Brownian motionsin a d-dimensional space. The law of the square of the radial distance from the origin of that process is indeed the same as the law of X(t) -- for special omegas. In other words, it's true that Feller's Sqrt process isequivalent to a Squared Radial OU process. But this does not yield a closed-form soln to the original problem under my definition. If somebody would like to argue for why a different defn is better or whyI'm out to lunch, please go ahead.
Last edited by Alan
on December 24th, 2011, 11:00 pm, edited 1 time in total.