First, our endowment (consumption) growth follows a slow

mean-reverting process. After the realization of a bad endowment shock, the expected consumption growth rate edges up only slightly because of the trend-reverting property, which makes the autocorrelation of the consumption growth process slightly negative but very close to zero.

In the OU model the stochastic random variable St follows a geometric

mean-reverting process given by the differential equation as:

He modelled temperature as a

mean-reverting process by adapting directly the Hull-White model.

The short-term variance of asset price follows a

mean-reverting process. A

mean-reverting process is introduced to allow for the common long-term volatility risk in the underlying asset price and counterparty's asset value, which differs from assumption that long-term volatility is constant in Wang et al.

A major difference between the two is that the LS model sets the default boundary as a constant K, while the CG model allows the default boundary to be a

mean-reverting process. Default occurs when the firm value hits the threshold K, or [l.sub.t] = ln(K/[V.sub.t]) = 0.

The authors consider that the amount of undervaluation X, is given by a

mean-reverting processIn what follows, we provide the solution when [([theta]).sub.t] is a

mean-reverting process:

Each country's exposure to disaster risk varies over time according to a

mean-reverting process. Risky countries command high risk premia: they feature a depreciated exchange rate and a high interest rate.

Thus, one way of testing the PPP is to test for the mean-reverting property of the nominal exchange rate that incorporates changes in relative prices into its

mean-reverting process, that is, testing for stationarity of the real exchange rate.

These results support the two-regime TAR specification for all five countries--a stationary

mean-reverting process for interest rate differentials outside the bands and a unit root process inside the bands.

Moreover, a comparison of a 30 year and 117 year time series analyses demonstrates that while in the shorter sample the hypothesis of a random walk cannot be rejected, in the longer it is, in favor of a

mean-reverting process. Therefore there are certain markets for which we should acknowledge that the random walk is not an adequate description of the processes involved.

The first model is a one-factor model in which the log of the spot price of the commodity is assumed to follow a

mean-reverting process. The second model assumes that the convenience yield is also stochastic and follows a

mean-reverting process.