The Discrete Time Case

  • Nicolas PrivaultEmail author
Part of the Lecture Notes in Mathematics book series (LNM, volume 1982)


In this chapter we introduce the tools of stochastic analysis in the simple framework of discrete time random walks. Our presentation relies on the use of finite difference gradient and divergence operators which are defined along with single and multiple stochastic integrals. The main applications of stochastic analysis to be considered in the following chapters, including func- tional inequalities and mathematical finance, are discussed in this elementary setting. Some technical difficulties involving measurability and integrability conditions, that are typical of the continuous-time case, are absent in the discrete time case.


Discrete Time Hedging Strategy Predictable Process Logarithmic Sobolev Inequality Covariance Identity 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.Department of MathematicsCity University of Hong KongHong Kong P.R. China

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