A textbook for a rigorous introduction to Stochastic Analysis with emphasis on stochastic differential equations I'm looking for a good textbook for an introduction to Stochastic Analysis, preferably one that focuses on rigour. I am familiar with measure theory and basic probability theory. The direction I am mostly interested in is stochastic differential equations.

personally i like Chung and Williams. Very clear and unambitious whilst maintaining rigour.

See also my recommended book list on www.markjoshi.com