This monograph aims to present and develop a general theory of stochastic integration where the integral is a non-linear function of the integrand. A discussion of the theory and corresponding stochastic calculus is given, providing a generalization of the works of Sznitman on L2-martingales, Le Jan and Watanabe on smooth martingales and Futjiwara and Kunita on the integral with respect to Levy processes.
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