Which cameras are best considered to perform in low lighting conditions that result in very low noise and grains, letting you to know that I have no limit to my budget?

a canon 550d paired with a f1.4 lens, dirt cheap and you"ll see better in the dark then with your own eyes. :)

Broad question, and really need to know more about the intended use/expectations. You've basically asked which car to buy that can go 100 miles per hour...

If you're looking at a small standard videocam, the Sony CX550V is hard to beat for low noise in bad light, same goes for any of the other 500 series Sonys with the R sensor, budget around $1K USD for a decent kit with extra batteries and such, dependign on which model you choose and accessories.

And for some shooting situations, a DSLR-V may offer a good choice.

If money is no object... well that's a different kettle of fish.

Ultimately a little more info on what you want to do with this camera would be rather helpful to get a useful answer... lots of good "tools" out there, some better for one "job:"over another.

if you're shooting film, then you can get fast lenses and stock. If you're shooting HD, then you can still use an Alexa/Red/Viper/Genesis/Cinealta/Varicam with fast lenses. If you're shooting in the prosumer level, a Canon 5D with f2 and less L glasses. Any other video camera and the same rule applies...but I don't think this really helps you unless you ask a much more specific question.

oops, I thought there was a "limited" budget but now I see it says no limit.
Anyways, I also can agree what Dave says about the 500 exmor r series of Sony, I have filmed a few times with a 520 model and it's a quite amazing camera for it's size, first time I filmed with it I couldn't believe what this tiny camera was capable off both in terms of low light, low noise, sharpness, color (which is not so artificially pumped up like other small handycams) and image stability, it's image stabilization makes it possible to walk around almost looking like your using a steadicam device, you have to see it to believe it. :).

If there's no budget limit, you could also consider the Arri Alexa or the RED One, which is now only being sold with the MX sensor. It really depend on what you want to use the camera for.

The DSLR cameras offer excellent low capabilities, but may have limitations which don't make them suitable for your production.

Thanks all of you for your response. Well, I am looking for a high performance camera in low lighting conditions particularly for indoor events, night shoots, studio and documentary. How about XDCAM series? Which of them performs best in low lighting, or they give the same output?

Anyone replying my post?