% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/internals.R
\name{ou_params}
\alias{ou_params}
\title{Compute exact Ornstein-Uhlenbeck discrete-time transition parameters}
\usage{
ou_params(kappa, sigma_psi)
}
\arguments{
\item{kappa}{Positive mean-reversion speed.}

\item{sigma_psi}{Positive continuous-time volatility.}
}
\value{
A named list with elements \code{alpha} and \code{tau}.
}
\description{
For the continuous-time OU SDE
\eqn{d\Psi_t = \kappa(\mu_\Psi - \Psi_t)\,dt + \sigma_\Psi\,dW_t},
the exact one-day transition is
\eqn{\Psi_n | \Psi_{n-1} \sim N(\mu_\Psi + \alpha(\Psi_{n-1}-\mu_\Psi), \tau^2)}
with \eqn{\alpha = e^{-\kappa}} and
\eqn{\tau^2 = \sigma_\Psi^2(1-e^{-2\kappa})/(2\kappa)}.
}
\examples{
ou_params(kappa = 0.05, sigma_psi = 0.10)
}
