Basic Itô calculus

Jacques Franchi and Yves Le Jan

in Hyperbolic Dynamics and Brownian Motion

Published in print August 2012 | ISBN: 9780199654109
Published online January 2013 | e-ISBN: 9780191745676 | DOI:

Series: Oxford Mathematical Monographs

Basic Itô calculus

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This chapter deals with the basic Itô calculus. Fundamental notions such as predictability, martingales and stopping times are introduced in the discrete case. The chapter then gives a short account of the necessary background on martingales and Brownian motion, and the chapter deals finally with the basic tools of Itô's calculus: the stochastic integral and the Itô change-of-variable formula.

Keywords: Brownian motion; martingales; stochastic integral; Itô calculus; Stratonovich integral

Chapter.  11588 words. 

Subjects: Mathematical and Statistical Physics

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