I'd use PSutil. To provide a practical example:
import psutil
for proc in psutil.get_process_list():
if proc.username == 'yourusername':
if myappname in proc.cmdline:
print 'App is running'
Alternatively, Red Hat use and maintain a Python module called python-linux-procfs , which natively parses /proc, to manage processes. it's not very well publicized, but provides some additional Linux-specific features (eg, scheduling class) which are sometimes useful.
http://pkgs.fedoraproject.org/gitweb/?p=python-linux-procfs.git