Stochastic Integrals

“To begin at the beginning: …”.- Stochastic integrals: Basic theory.- Stochastic integration and discontinuous martingales.- Martingales, the Malliavin calculus and Hörmander's theorem.- On a representation of local martingale additive functionals of symmetric diffusions.- Set-parametered martingales and multiple stochastic integration.- Generalized ornstein — Uhlenbeck processes as limits of interacting systems.- Weak and strong solutions of stochastic differential equations: Existence and stability.- On the decomposition of solutions of stochastic differential equations.- A differential geometric formalism for the ito calculus.- Homogenization and stochastic parallel displacement.- Bessel processes and infinitely divisible laws.- Euclidean quantum mechanics and stochastic integrals.- The malliavin calculus and its applications.- The probability functionals (Onsager-machlup functions) of diffusion processes.- Ito and girsanov formulae for two parameter processes.- Lp-inequalities for two-parameter martingales.- Dirichlet processes.- Brownian motion, negative curvature, and harmonic maps.- Local behaviour of hilbert space valued stochastic integrals and the continuity of mild solutions of stochastic evolution equations.- Some markov processes and markov fields in quantum theory, group theory, hydrodynamics and C*-algebras.