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Stochastic Analysis in Discrete and Continuous Settings - With Normal Martingales (Paperback, 2009 ed.)
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Stochastic Analysis in Discrete and Continuous Settings - With Normal Martingales (Paperback, 2009 ed.)
Series: Lecture Notes in Mathematics, 1982
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This monograph is an introduction to some aspects of stochastic
analysis in the framework of normal martingales, in both discrete
and continuous time. The text is mostly self-contained, except for
Section 5.7 that requires some background in geometry, and should
be accessible to graduate students and researchers having already
received a basic training in probability. Prereq- sites are mostly
limited to a knowledge of measure theory and probability,
namely?-algebras,expectations,andconditionalexpectations.Ashortint-
duction to stochastic calculus for continuous and jump processes is
given in Chapter 2 using normal martingales, whose predictable
quadratic variation is the Lebesgue measure. There already exists
several books devoted to stochastic analysis for c- tinuous
di?usion processes on Gaussian and Wiener spaces, cf. e.g. [51],
[63], [65], [72], [83], [84], [92], [128], [134], [143], [146],
[147]. The particular f- ture of this text is to simultaneously
consider continuous processes and jump processes in the uni?ed
framework of normal martingales.
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