GLOBAL MARKETS-Stock markets recover from recent weakness; oil still down

* Oil extends slide, close to $45 a barrel* Prospect of ECB actions lifts shares in Europe, U.S.* Dollar gains vs yen and euro in choppy trade(Updates to open of U.S. trading, changes byline and dateline, previously LONDON)By Ryan VlastelicaNEW YORK, Jan 13 (Reuters) - Stock markets around the world rose on Tuesday, rebounding after a recent bout of weakness as investors bet that there would be ec