Introduction -- Some Mathematical Preliminaries -- Ito Integrals -- Ito Processes and the Ito Formula -- Stochastic Differential Equations -- The Filtering Problem -- Diffusions: Basic Problems -- Other Topics in Diffusion Theory -- Applications to Boundary Value Problems -- Applications to Optimal Stopping -- Application to Stochastic Control -- Application to Mathematical Finance -- Appendix A: Normal Random Variables -- Appendix B: Conditional Expectations -- Appendix C: Uniform Integrability and Martingale Convergence -- Solutions and Additional Hints to Some of the Exercises -- Bibliography -- List of Frequently Used Notation and Symbols -- Index.

This book gives an introduction to the basic theory of stochastic calculus and its applications. Examples are given throughout the text, in order to motivate and illustrate the theory and show its importance for many applications in e.g. economics, biology and physics. The basic idea of the presentation is to start from some basic results (without proofs) of the easier cases and develop the theory from there, and to concentrate on the proofs of the easier case (which nevertheless are often sufficiently general for many purposes) in order to be able to reach quickly the parts of the theory which is most important for the applications. The new feature of this 5th edition is an extra chapter on applications to mathematical finance.

English.