In order to provide a user access to run processes in PeopleSoft provide a value for primary permission list as well as process profile permission list on the general tab on the user profile page.
Following is from Peoplebooks.
PrimaryPermissionList
PeopleSoft determines which data permissions to grant a user by examining the primary permission list and row security permission list. Which one is used varies by application and data entity (employee, customer, vendor, business unit, and so on). Consult your PeopleSoft application documentation for more details. PeopleSoft also determines mass change and definition security permissions from the primary permission list.
PrimaryPermissionList
PeopleSoft determines which data permissions to grant a user by examining the primary permission list and row security permission list. Which one is used varies by application and data entity (employee, customer, vendor, business unit, and so on). Consult your PeopleSoft application documentation for more details. PeopleSoft also determines mass change and definition security permissions from the primary permission list.
ProcessProfilePermissionList
The process profile contains the permissions that a user requires for running batch processes through PeopleSoft Process Scheduler. For example, the process profile authorizes users to view output, update run locations, restart processes, and so on. Only the process profile comes from this permission list, not the list of process groups.
The process profile contains the permissions that a user requires for running batch processes through PeopleSoft Process Scheduler. For example, the process profile authorizes users to view output, update run locations, restart processes, and so on. Only the process profile comes from this permission list, not the list of process groups.