Stochastic Differential Equations: An Introduction with Applications

Bernt K. Oksendal

ISBN 10: 3540637206 / ISBN 13: 9783540637202

Editore: Springer, 2002

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Codice articolo S_444289915

Dati bibliografici

• Titolo: Stochastic Differential Equations: An Introduction with Applications
• Editore: Springer
• Data di pubblicazione: 2002
• Lingua: Inglese
• ISBN 10: 3540637206
• ISBN 13: 9783540637202
• Rilegatura: Paperback
• Edizione: seconda edizione
• Condizione: Good

Descrizione articolo

Riassunto

This text 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, for example, economics, biology and physics. The 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 fifth edition is an extra chapter on applications to mathematical finance.

Contenuti

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.