This book offers a rigorous and self-contained approach to the theory of stochastic integration
and stochastic calculus within the general framework of continuous semimartingales. The main
tools of stochastic calculus including Itô's formula the optional stopping theorem and the
Girsanov theorem are treated in detail including many important applications. Two chapters are
devoted to general Markov processes and to stochastic differential equations with a complete
derivation of Markovian properties of solutions in the Lipschitz case. Numerous exercises help
the reader to get acquainted with the techniques of stochastic calculus.
