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stochastic processes - Covariance of Ornstein - Uhlenbeck Process ...
Proof that the Ornstein-Uhlenbeck process is continuous. 11. How to calculate the PSD of a stochastic ...
stochastic processes - Fokker-Planck equation for Ornstein-Uhlenbeck ...
$\begingroup$ I've never learned the definitions of forward equation versus backward equation unfortunately. What I do know is I would find the transition kernel in this case by solving $\frac{\partial f}{\partial t} - \Delta f + \alpha x \cdot \nabla f = 0$ using the Fourier transform and reading off the transition kernel from the solution.
stochastic processes - Difference between Ornstein-Uhlenbeck, Vasicek ...
Ornstein-Uhlebeck = Vasicek (only difference being that Vasicek can sometimes have (deterministic) non-constant reversion speed parameter, whilst Ornstein-Uhlenbeck has all parameters constant by definition). Exponetial Vasicek = EMR. The term $4 \alpha$ in the denominator looks like a typo, should be $2 \alpha$ Long Answer:
stochastic processes - Implementing Ornstein–Uhlenbeck in Matlab ...
The Wikipedia article you cite provides everything you need to evaluate the analytical solution of the Ornstein–Uhlenbeck process. However, for a beginner, I agree that it may not be very clear. 1. Simulating the Ornstein–Uhlenbeck process. You should first be familiar with how to simulate this process using the Euler–Maruyama method. The ...
Autocovariance of Ornstein–Uhlenbeck and AR (1) processes
The autocovariance of an Ornstein–Uhlenbeck process $$ dX(t) = \\theta (\\mu - X(t))dt + \\sigma dW(t) $$ is given on Wikipedia as $$ \\operatorname{Cov}(X(s),X(t ...
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