In the theory of inflation, demand pull inflation and cost push inflation are usually one off shocks. However, a series of such shocks may lead people to assume that inflation is a permanent feature of the economy, in which case they will modify their economic behaviour accordingly, based on their expectation of future inflation rates. For instance, they may begin demanding larger pay raises - this in itself acts as a cost push, leading firms to push their prices higher, and thus to another round of pay-raises. This "wage-price spiral" builds some inflation directly into the economy! The theory of adaptive expectations was popular in the 1980s, as an explanation of some aspects of the economic crisis that the West went through after the 1970s oil shock. The fact that some countries, particularly the UK, took until the 1990s to achieve stable low inflation rates again suggests there may well be something in the idea.
An alternative theory of how expectations are formed is rational expectations.