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Hyperbolic Dynamics and Brownian MotionAn Introduction$
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Jacques Franchi and Yves Le Jan

Print publication date: 2012

Print ISBN-13: 9780199654109

Published to Oxford Scholarship Online: January 2013

DOI: 10.1093/acprof:oso/9780199654109.001.0001

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Basic Itô calculus

Basic Itô calculus

(p.124) Chapter Six: Basic Itô calculus
Hyperbolic Dynamics and Brownian Motion

Jacques Franchi

Yves Le Jan

Oxford University Press

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

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