Your IP address may change whenever there is a disconnect or it expires I believe, at least that's how it works at my house with Comcast cable service-- but if you're suspecting an unauthorized person on your network, there are a few things you can do. First, I would assess the area you live in, is it urban, suburban, rural, etc.? Does a high volume of traffic pass near your house often? I've seen people pulling over in side streets to check email on unprotected networks. But you say you have security, so maybe someone living near you is hacking your network. What kind of security do you have set up? I would recommend at least WEP encryption, but WPA is much stronger. Another helpful security option available on most routers is MAC address filtering, which will only allow computers with a specific physical address to access your network. This, like any other security option, can be thwarted, but if you have encryption in place and switch keys every now and then on top of MAC address filtering you should be pretty secure (hackers will just realize its a pain in the ass to stay connected to your network haha). If you would like details on how to set up some more security, I'd be glad to try and help. And a call to your ISP would be wise to clear things up with them.
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