Checking to see who a process belongs to

I can check to see if a process is running with

tell application "System Events"
	if exists process "Activity Monitor" then
		display dialog "Running"
	else
		display dialog "Not running"
	end if
end tell

but how can I tell who it belongs to? I need to know if the active user has an app open.

--Non-working example
if exists process "Activity Monitor" with user "maeks84" then

Does UNIX have to get involved in this?

Missed it earlier, but I just discovered that “System Events” only seems to check the process names of the current user. I can have Activity Monitor running in a second account, but it is not detected by the script even though it shows up in the Activity Monitor. Is there anyway to make “System Events” catch the process no matter who runs it as well?