We have assumed the short-term interest rate has a lognormal distribution at any time horizon. This means we require only a mean and standard deviation to fully specify its distribution. However, in the BK model, three factors are required to describe the short-term interest rate process - the target rate, mean reversion speed and local volatility. This means that for a given time horizon, the solution is not unique and the distribution of short- term interest rates may be matched by a family of possible processes.
These processes will differ in their mean reversion and local volatility characteristics. Strong mean reversion means a move away from the target rate is quickly reversed , which is not the case for weaker mean reversion. Hence, a narrow (wide) distribution of the short-term interest rate in the future may result from either strong (weak) mean reversion or low (high) local volatility.