Solution to a Geometric Ornstein Uhlenbeck Process $dX_t = \kappa(\theta - X_t)dt + \sigma X_t dW_t$ - Quantitative Finance Stack Exchange most recent 30 from quant.stackexchange.com 2019-08-23T11:39:26Z https://quant.stackexchange.com/feeds/question/45083 http://www.creativecommons.org/licenses/by-sa/3.0/rdf https://quant.stackexchange.com/q/45083 2 Solution to a Geometric Ornstein Uhlenbeck Process $dX_t = \kappa(\theta - X_t)dt + \sigma X_t dW_t$ Freelunch https://quant.stackexchange.com/users/24306 2019-04-13T11:33:00Z 2019-05-02T04:21:35Z <p>I've been searching for the solution to the modified Ornstein-Uhlenbeck process <span class="math-container">\begin{equation*} dX_t = \kappa(\theta - X_t)dt + \sigma X_t dW_t \end{equation*}</span> but it surprisingly hard to find. The <a href="https://en.wikipedia.org/wiki/Ornstein%E2%80%93Uhlenbeck_process#Generalizations" rel="nofollow noreferrer">Wikipedia page</a> on the OU-process even mentions that a closed form solution exists but doesn't provide any reference. Any help?</p> https://quant.stackexchange.com/questions/45083/-/45095#45095 2 Answer by Magic is in the chain for Solution to a Geometric Ornstein Uhlenbeck Process $dX_t = \kappa(\theta - X_t)dt + \sigma X_t dW_t$ Magic is in the chain https://quant.stackexchange.com/users/35546 2019-04-13T20:38:56Z 2019-04-13T20:38:56Z <p>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.</p>