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Theory of stochastic differential equations with jumps and applications. (English) Zbl 1070.60002
Mathematical and Analytical Techniques with Applications to Engineering. New York, NY: Springer (ISBN 0-387-25083-2/hbk; 978-1-4419-3771-1/pbk; 978-0-387-25175-2/ebook). xx, 434 p. (2005).
This monograph is mostly a compilation of definitions and of theorems and their proofs concerning Itô stochastic differential equations (SDE). In the first five chapters, after providing basic information on stochastic processes and Itô integrals, existence and uniqueness theorems and convergence theorems for both strong solutions and weak solutions of SDE are presented and proved under a variety of different conditions on the coefficients of the SDE. The remaining seven chapters concentrate on SDE arising in areas of application (including finance [especially option pricing and optimal consumption], filtering, optimal control, and population control) with emphasis on theory and proofs rather than implementation in applications.

MSC:
60-02 Research exposition (monographs, survey articles) pertaining to probability theory
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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