In this paper, we discuss the problem of modeling a graph signal on a directed graph when observing only partially the graph signal. The graph signal is recovered using a learned graph filter. The novelty is to use the random walk operator associated to an ergodic random walk on the graph, so as to define and learn a graph filter, expressed as a polynomial of this operator. Through the study of different cases, we show the efficiency of the signal modeling using the random walk operator compared to existing methods using the adjacency matrix or ignoring the directions in the graph.