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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

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

Jacques Franchi

Yves Le Jan

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199654109.003.0006

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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