# Solution to a Geometric Ornstein Uhlenbeck Process $dX_t = \kappa(\theta - X_t)dt + \sigma X_t dW_t$

I've been searching for the solution to the modified Ornstein-Uhlenbeck process $$\begin{equation*} dX_t = \kappa(\theta - X_t)dt + \sigma X_t dW_t \end{equation*}$$ but it surprisingly hard to find. The Wikipedia page on the OU-process even mentions that a closed form solution exists but doesn't provide any reference. Any help?

## 1 Answer

This is covered in the Introduction to Stochastic Calculus with applications by Klebaner, though you can find very similar presentation in the answers to the question that Gordon referenced in the comment.

• Do you remember in which chapter or by what name the equations is occurs in the book? – Freelunch Apr 14 '19 at 11:26
• Section 5.3 solutions to linear SDEs – Magic is in the chain Apr 14 '19 at 15:15