Most Indians have this habit while speaking in English. It's not stammering that I'm aware of. It's not stuttering or bumbling either. I'm not sure what is it called.
The speech goes like this...
Hello everyone. I'm Maulik and here I am to present a..... our company's .....a....... balancesheet for the year of 2014-15. As we see, we are going through ...a.......lots of ups and downs in a......
How is 'a' pronounced there? It's the same way we pronounce this indefinite article with any noun. So, it's 'a' in 'a car'.
It's not just with Indians, I have seen many foreigners (even natives) with this habit but the frequency is quite less.
The video: (Check at 00:56 and 1:01) - Note: Irfan's English is still better! The people I'm talking about have loud and clear 'a......a....a'.
Listen it carefully. There are several such pauses. I'm not sure whether the narrator is native - http://www.bbc.com/news/world-asia-27577537