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We present new theoretical results on the fractional Brownian motion, including different definitions (and their relationships) of the stochastic integral with respect to this process, Girsanov theorem, Clark representation formula, Itô formula and so on. Several applications (such as non-linear filtering theory, queuing networks, mathematical finance) are given as applied examples of these theoretical results.
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Decreusefond et al. (1998) studied this question.
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