Abstract
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.
Keywords
- Discrete Time
- Hedging Strategy
- Predictable Process
- Logarithmic Sobolev Inequality
- Covariance Identity
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© 2009 Springer-Verlag Berlin Heidelberg
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Privault, N. (2009). The Discrete Time Case. In: Stochastic Analysis in Discrete and Continuous Settings. Lecture Notes in Mathematics(), vol 1982. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02380-4_2
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DOI: https://doi.org/10.1007/978-3-642-02380-4_2
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-02379-8
Online ISBN: 978-3-642-02380-4
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