It is possible to catch Pokemon while sitting at home, but it is very unlikely that you will. There are some things that you can do to increase the odds in which Pokemon can be captured at home, but most of the time you will find that you need to be walking around in order to capture any Pokemon.
If you are looking to capture Pokemon at home, there are some steps you can take to increase the odds.
- Use Incense – This draws pokemon to you, rather than you having to walk to them. This can be used while sitting at home and will cause Pokemon to randomly appear right beside you on the map. Turning the app off and on again often increases the spawn rate of this.
- Living next to a Poke stop – This of course is a hard thing, but if you are lucky enough you will find that you get a lot of trainers placing lures and you can take advantage of this in the same way as you would with incense.
- Walking around – If you have a big enough house and an accurate GPS you can walk around your home in circles and make some progress playing the game.
There may be some other methods in which you can do this, but they will not be legitimate and could run the risk of your account getting banned.