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?
Solution to a Geometric Ornstein Uhlenbeck Process $dX_t = \kappa(\theta - X_t)dt + \sigma X_t dW_t$
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2$\begingroup$ Have a look of this question. $\endgroup$– GordonApr 13, 2019 at 16:37
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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.
answered Apr 13, 2019 at 20:38
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$\begingroup$ Do you remember in which chapter or by what name the equations is occurs in the book? $\endgroup$ Apr 14, 2019 at 11:26
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$\begingroup$ Section 5.3 solutions to linear SDEs $\endgroup$ Apr 14, 2019 at 15:15