Stochastic analysis in discrete and continuous settings : with normal martingales / Nicolas Privault

The author presents several aspects of stochastic analysis for discrete and continuous-time normal martingales. Normal martingales constitute a class of stochastic processes which contains both continuous and pure jump processes including for example the standard Brownian motion, the compensated Poisson process and some “unusual” processes like the so-called Azéma martingales. In the literature, several authors have described a stochastic analysis and especially Malliavin's calculus either for continuous diffusion processes defined on Gaussian and Wiener spaces, or for jump processes. The particular feature of this volume of the Lecture Notes in Mathematics is to consider a framework (normal martingales) for which a stochastic analysis can be derived simultaneously for continuous and for jump processes. Another achievement of this book is to deal with both discrete and continuous-time processes. Especially a Malliavin calculus for some discrete time processes is presented which constitutes a material interesting in itself. (Zentralblatt)

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