A solution to the general stochastic differential equation (SDE) can yield a time-independent probability density function (pdf) while maintaining a nonstationary stochastic process. It is possible to have a constant distribution function with a correlation function that depends on both time variables, indicating nonstationarity. An example provided is a Gaussian process with a mean of zero and standard deviation of one, where the correlation function is defined as f(s,t) = 1/(1+|s²-t²|). The discussion raises questions about how to compute this correlation and the apparent contradiction of having a time-independent pdf alongside a time-dependent correlation function. Understanding these concepts is crucial for exploring the dynamics of stochastic processes.
