From Wikipedia, the free encyclopedia
In statistics, a continuous time random walk with drift and random jumps at every point in time
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:
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
[edit]This article does not cite any sources. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. Find sources: "Generalized Wiener process" – news · newspapers · books · scholar · JSTOR (February 2010) (Learn how and when to remove this message) |
![]() | This statistics-related article is a stub. You can help Wikipedia by expanding it. |
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url