Itô's stochastic calculus and its applications (Q2734981)

The basic notions of modern stochastic calculus are presented and developed here in the form of a lecture, with all definitions, main results in general framework, and several examples, but without proofs. This constitutes a sort of summary of the classical book by Ikeda and Watanabe. So there are successively explained in a both clear, precise and synthetic way the following items: Wiener and Poisson processes, semimartingales, stochastic integrals, general Itô's formula, time changes, change of drift, Black-Scholes formula, stochastic differential equations in \(\mathbb{R}^d\), diffusions and flows of diffeomorphisms in \(\mathbb{R}^d\), Malliavin calculus, reflected diffusions, stochastic differential equations in manifolds, moving frames, probabilistic representation of heat kernels, Brownian motions on Lie groups.NEWLINENEWLINEFor the entire collection see [Zbl 0961.60001].