Probability density function
Stochastic methods use distribution functions to decribe the fluctuacting scalars in a turbulent field.
The distribution function of a scalar is the probability of finding a value of
The probability of finding in a range is
The probability density function (PDF) is
where is the probability of being in the range . It follows that
Integrating over all the possible values of . The PDF of any stochastic variable depends "a-priori" on space and time.