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Transformation of time dependent probability distributions

Given a distribution of position at time zero, P(x, 0), one obtains the distribution at a subsequent time t, P(x, t), by solving the appropriate evolution equation. Often this is a very difficult problem. However, sometimes, it is relativity easy to obtain the exact time dependent low order moments. We present methods to approximate P(x, t) using the initial probability distribution and exact low order time dependent moments.