There is a command called nohup that you can use to start the program. The program name stands for 'no HUP'. Output is redirected to a file, and logging out will not cause the HUP signal begin sent to the background program.
The nohup command is one of the GNU coreutils. Read through the `info nohup` texinfo manual for details. The 'man nohup' may not contain all the details that are in the info page.