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.

Klappentext

Also called Ito calculus, the theory of stochastic integration has applications in virtually every scientific area involving random functions. This introductory textbook provides a concise introduction to the Ito calculus.

From the reviews:

"Introduction to Stochastic Integration is exactly what the title says. I would maybe just add a 'friendly' introduction because of the clear presentation and flow of the contents." --THE MATHEMATICAL SCIENCES DIGITAL LIBRARY

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.