$$\frac{1}{\cosh(x)} = \frac{2}{e^x + e^{-x}}$$
is similar to scaled normal distribution $e^{-x^2}$ in general shape. We know that central limit theorem say that the summation of independent identical random variables will lead to a distribution of the scaled $e^{-x^2}$.
Question: which type stochastic process or random walks can led to a distribution of $\frac{1}{\cosh(x)}$ ?