Importance sampling, Fokker-Planck and Langevin equations

A stochastic process is simply a function of two variables, one is the time, the other is a stochastic variable $X$, defined by specifying

1. the set $\left\{x\right\}$ of possible values for $X$;
2. the probability distribution, $w_X(x)$, over this set, or briefly $w(x)$

The set of values $\left\{x\right\}$ for $X$ may be discrete, or continuous. If the set of values is continuous, then $w_X (x)$ is a probability density so that $w_X (x)dx$ is the probability that one finds the stochastic variable $X$ to have values in the range $[x, x +dx]$ .

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