I bought something similar to EasyCap a while ago to grab captures from my DVR..
StarTech SVID2USB2 USB 2.0 Video Capture Cable
I don't know how/if it works for Streaming, but I have found it very useful to capture video from my DVR straight to my computer which saves me a ton of time since I no longer have to capture to a video camera, then back out to a computer. It hooks directly up!
Again, not sure of its streaming abilities, but it works well for what I have been using it for and I thought I'd throw it out there in case it could work for you.