# Convergence of Sarsa($\lambda$)

Is there any theorem on the convergence of the Sarsa($$\lambda$$) Algorithm?

I am currently working through the theory of Reinforcement Learning with the lecture by David Silver and the book of Sutton & Barto. I could not find an answer to my question. I found comments and theorems on the convergence of TD($$\lambda$$) and one-step Sarsa, but nothing for Sarsa($$\lambda$$). Same result after hitting Google for an hour. Does the convergence follows naturally as Sarsa($$\lambda$$) is basically the equivalent of TD($$\lambda$$) in the control setting?

Any help appreciated.