3.6. Consider a general SDE dX = (X)dt+(X)dW . Assuming a steady state PDF exists for the ensemble of realizations, show that the steady state

3.6. Consider a general SDE dX = μ(X)dt+σ(X)dW . Assuming a steady state PDF exists for the ensemble of realizations, show that the steady state PDF may be written as p(x) =

A D(x)

exp

μ(x)

D(x)

dx

, where D(x) = 12

σ(x)2 and A is a normalization constant.

4- 3- 2- 0 1 2 3 4 5 6 7 8 9 10 time t