The theory of stochastic integration, also called the Ito calculus, has a large spectrum of applications in virtually every scientific area involving random functions. This introductory textbook on stochastic integration provides a concise introduction to the Ito calculus, and covers the constructions of Brownian motion, stochastic integrals for Brownian motion and martingales, the Ito formula, multiple Wiener-Ito integrals, stochastic differential equations, and applications to finance, filtering theory, and electric circuits.

Provides a concise introduction to the theory of stochastic integration, also called the Ito calculus Closes the gap between more technically advanced books like Karatzas and Shreve (Springer) and less rigourous but more intuitive approaches such as that of Thomas Mikosch (World Scientific) Each chapter includes a variety of exercises designed to help the reader further understand the material Contains an unusually diverse selection of examples, and an attractive selection of topics Includes supplementary material: sn.pub/extras

Zusammenfassung
It was the beginning of the It o calculus, the counterpart of the LeibnizNewton calculus for random functions. The It o formula is the chain rule for the Itocalculus.Butitcannotbe expressed as in the LeibnizNewton calculus in terms of derivatives, since a Brownian motion path is nowhere di?erentiable.

Inhalt
Brownian Motion.- Constructions of Brownian Motion.- Stochastic Integrals.- An Extension of Stochastic Integrals.- Stochastic Integrals for Martingales.- The Itô Formula.- Applications of the Itô Formula.- Multiple Wiener-Itô Integrals.- Stochastic Differential Equations.- Some Applications and Additional Topics.