Rényi entropy rate for Gaussian processes

In this paper, we introduce the definition of the conditional Rényi entropy for continuous random variables and show that the so-called chain rule holds. Then, we use this rule to obtain another relation for getting the rate of Rényi entropy. Using this relation and properties of the Rényi entropy we obtain the Rényi entropy rate for stationary Gaussian processes. Finally, we show that the bound for the Rényi entropy rate is simply the Shannon entropy rate and that the Rényi entropy rate reduces to the Shannon entropy rate as image.