Advanced maths students have been waiting for this， the third edition of a text that deals with one of the fundamentals of their field。 This book contains a systematic treatment of probability from the ground up， starting with intuitive ideas and gradually developing more sophisticated subjects， such as random walks and the Kalman-Bucy filter。 Examples are discussed in detail， and there are a large number of exercises。 This third edition contains new problems and exercises， new proofs， expanded material on financial mathematics， financial engineering， and mathematical statistics， and a final chapter on the history of probability theory。