Introduction to Stochastic Integration

Hui-Hsiung Kuo

ISBN 10: 0387287205 / ISBN 13: 9780387287201

Editore: Springer New York, Springer New York, 2005

Riguardo questo articolo

Druck auf Anfrage Neuware - Printed after ordering - In the Leibniz-Newton calculus, one learns the di erentiation and integration of deterministic functions. A basic theorem in di erentiation is the chain rule, which gives the derivative of a composite of two di erentiable functions. The chain rule, when written in an inde nite integral form, yields the method of substitution. In advanced calculus, the Riemann-Stieltjes integral is de ned through the same procedure of 'partition-evaluation-summation-limit' as in the Riemann integral. In dealing with random functions such as functions of a Brownian motion, the chain rule for the Leibniz-Newton calculus breaks down. A Brownian motionmovessorapidlyandirregularlythatalmostallofitssamplepathsare nowhere di erentiable. Thus we cannot di erentiate functions of a Brownian motion in the same way as in the Leibniz-Newton calculus. In 1944 Kiyosi It o published the celebrated paper 'Stochastic Integral' in the Proceedings of the Imperial Academy (Tokyo). It was the beginning of the It o calculus, the counterpart of the Leibniz-Newton calculus for random functions. In this six-page paper, It o introduced the stochastic integral and a formula, known since then as It o's formula. The It o formula is the chain rule for the It ocalculus.Butitcannotbe expressed as in the Leibniz-Newton calculus in terms of derivatives, since a Brownian motion path is nowhere di erentiable. The It o formula can be interpreted only in the integral form. Moreover, there is an additional term in the formula, called the It o correction term, resulting from the nonzero quadratic variation of a Brownian motion.

Codice articolo 9780387287201

Dati bibliografici

• Titolo: Introduction to Stochastic Integration
• Editore: Springer New York, Springer New York
• Data di pubblicazione: 2005
• Lingua: Inglese
• ISBN 10: 0387287205
• ISBN 13: 9780387287201
• Rilegatura: Taschenbuch
• Condizione: Neu
• Dimensioni: 235 L x 155 A x 17 P (millimetri) 235 millimetri di larghezza per 155 millimetri di altezza per 17 millimetri di profondità
• Peso: 452 grammi

Descrizione articolo

Riassunto

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

Informazioni sull?autore

Hui-Hsiung Kuo is the Nicholson Professor of Mathematics at Louisiana State University.