Hello Swati,
Like Brain mentioned, Job is always initiated by the account in which service is running.
Job "triggered by" and "initiated by" both are different. Trace log is generated from the point when job is initiated by jobserver, there is no way trace log can have "triggered by" details.
If job is executed from scheduler, batch file will have user name, but its useless if you are trying to find out who executed batch file.