In statistics, a generalized Wiener process (named after Norbert Wiener) is a continuous time random walk with drift and random jumps at every point in time. Formally:
a ( x , t ) d t + b ( x , t ) η d t {\displaystyle a(x,t)dt+b(x,t)\eta {\sqrt {dt}}}
where a and b are deterministic functions, t is a continuous index for time, x is a set of exogenous variables that may change with time, dt is a differential in time, and η is a random draw from a standard normal distribution at each instant.
See also Wiener process
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