Manning and Schütze argue that, even though not quite correct, language text can be modeled as stationary, ergodic random processes BIBREF29, an assumption that we follow. Moreover, given the diversity of language production, we assume this stationary ergodic random process with finite alphabet $\mathcal {A}$ denoted $X = \lbrace X_i, -\infty < i < \infty \rbrace $ is non-null in the sense that always $P(x_{-m}^{-1}) > 0$ and

This is sometimes called the smoothing requirement. 
 Question: Is the assumption that natural language is stationary and ergodic valid?
It is not completely valid for natural languages because of diversity of language - this is called smoothing requirement.