Protter, Philip E. Stochastic integration and differential equations. 2nd ed. (English) Zbl 1041.60005 Applications of Mathematics 21. Berlin: Springer (ISBN 3-540-00313-4/hbk; 978-3-642-05560-7/pbk). xiii, 415 p. (2004). In the new edition several changes have been made, most of them are inclusions of results achieved since the appearance of the first edition (1990; Zbl 0694.60047). In particular, Chapter III, “Semimartingales and decomposable processes”, has been rewritten. Now the notion of predictability and R. Bass’ proof of the Doob-Meyer decomposition theorem are used where before the presentation had been based on Meyer’s notion of natural processes. A section on compensators is added. In Chapter IV the treatment of martingale representation now includes the Jacod-Yor theorem and a section on sigma martingales. Chapter V has a new section, entitled “Eclectic useful results on stochastic differential equations”. Chapter VI, “Expansions of filtrations”, is altogether new. Another addition are exercises, to be found at the end of each chapter. Altogether I agree with the previous reviewer, the book provides an excellent basis for lecturing or self-teaching. Reviewer: Evelyn Buckwar (Berlin) Cited in 1 ReviewCited in 889 Documents MathOverflow Questions: Is the stochastic integral invariant under equivalent change of probability? MSC: 60-02 Research exposition (monographs, survey articles) pertaining to probability theory 60H05 Stochastic integrals 60G07 General theory of stochastic processes 60H10 Stochastic ordinary differential equations (aspects of stochastic analysis) Keywords:stochastic integration; semimartingales; stochastic differential equations; local times; stochastic flows of diffeomorphisms; Lévy area formula; sigma martingales; expansion of filtrations Citations:Zbl 0694.60047 × Cite Format Result Cite Review PDF