Before I saw this questions and its answers, I made a little bash script. This is still useful, if you don't have root rights and acct isn't installed or you don't invoke your command directly (in my case: I use a gui to setup background processes). You need to get the PID before running (anyone interested in adding it into the script? :)
echo "Checking run time"
read -p "What is the pid? " PID
while true; do
# sleep needed! used to reduce cpu usage and mass of output
ps -eo uid,pid,etime | egrep '$PID' | egrep '$UID'
With this, find the PID of PROCESS_NAME
ps aux | awk 'NR == 1 || /PROCESS_NAME/'
Actually I tried combining USER-ID and PID to make the script non-ambigious, but it's not that easy...
ps -eo uid,pid,etime | egrep '$UID[[:space:]]$PID' don't seem to work always...