On a Windows server which is in a domain, I have a script I run from scheduled tasks.

I want this script to be run under a mydomain\peter user account. It is simple to do it with scheduled tasks, if you know Peter's password. And once done, the script stops when Peter decides to (or has to) change his password.

On Linux, a cron job can be run with whatever user account without having to know the corresponding password. And root can run anything on behalf on another user (with su and sudo).

Any way to do this with Windows?

My need is for a old Windows 2003 server, but I can manage to run it from another computer.