The term hysteresis is broadly used in economics to describe a persistent deviation from an economic equilibrium, especially after severe economic shocks. See for example the article in the Financial Times which claims that the British productive capacity will be permanently damaged as a result of the recent economic crisis.
http://www.ft.com/cms/s/0/e11f8430-9660-11de-84d1-00144feabdc0.html
However, this definition of hysteresis is in fact not correct in physical or mathematical terms. The formal definition of hysteresis refers to systems that have a ‘memory’, which means that the observed data today are dependent on events that occurred in the past. For example, a consequence of the efficient market hypothesis (EMH) is that markets, for example stock markets, do not have a memory, or in other words, all past information is instantaneously incorporated in the current stock prices. This means that one cannot make a profit from looking at past stock prices and extrapolate the findings to predict future stock prices. However, econometric tests of the EMH show that there are deviations from the EMH, indicating that the market may in some cases in fact have a memory. Following the EMH, the stock prices should follow a log-normal probability distribution. In reality, however, the returns of stocks are negatively skewed: there are more observations in the left-hand tail than in the right hand tail, and tails of the distribution are fatter than predicted by the normal distribution. This condition is also called leptokurtosis and is a consequence of the fact that the EMH underestimates the frequency of large price changes and that the standard deviation of stock prices is not constant (so called volatility clustering).
For a more formal discussion of hysteresis see for example:
http://math.gmu.edu/~harbir/CSM-08-03.pdf