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In this second edition, we have included additional material for use in modern applications of stochastic calculus in finance and biology; in particular, the section on infinitely divisible distributions and stable laws in Chap. 1, Lévy processes in Chap.2, the Itô-Lévy calculus in Chap.3, and Chap.4. Finally, a new appendix has been added that includes basic facts about semigroups of linear operators.We have also made an effort to improve the presentation of parts already included in the first edition, and we have corrected the misprints and errors we have been made aware of by colleagues and students during class use of the book in the intervening years.We are very grateful to all those who helped us in detecting them and suggested possible improvements.
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