One way to find out the owner of a process is to add the missing Owner property to process objects:
$processes = Get-WmiObject Win32_Process –Filter "name='notepad.exe'"
$appendedprocesses = foreach ($process in $processes) {
Add-Member -MemberType NoteProperty -Name Owner -Value (
$process.GetOwner().User) -InputObject $process -PassThru }
$appendedprocesses | ft name, owner
A loop adds the necessary Owner property. The resulting objects now show the owner. You could then use the information in Owner to selectively stop all processes owned by a specific user.