How to check if process with pid X is the one you expect

In our application, we start some background processes. The pid of these processes is saved to a file. pids values are re-used when the maximum is reached or when the system is rebooted. How can I reliably check that the process with pid X is still the same process for which X was stored. I've read https://serverfault.com/questions/366474/whats-a-proper-way-of-checking-if-a-pid-is-running and https://stackoverflow.com/questions/3043978/how-to-check-if-a-process-id-pid-exists but these solutions never check if the process that has pid X is the still same process as the one for which the pid was stored. I need this info to reliably * check the process is still running * kill the process without risking to kill a different process that now has pid X related https://serverfault.com/questions/279178/what-is-the-range-of-a-pid-on-linux-and-solaris I will post my current solution. I'd like to know if it's a sensible approach and if there are better ways to do this.