Stochastic Analysis and Random Maps in Hilbert Space
Andrey Anatoliyevich Dorogovtsev · 1994
Part 1 Stochastic calculus: preliminaries (L2-theory) smooth open sets the localization of the extended stochastic integral and the stochastic derivative stochastic integrals with respect to Gaussian random measures, Sobolev spaces on infinitely-dimensional domain. Part 2 Random maps in Hilbert space: the definition of a random map Gaussian strong random operators the integral representation of random maps. Part 3 The composition of random maps: the reasons random multi-linear Hilbert-Schmidt forms of the generalized Gaussian random elements the action of random map on random elements bounded random operators generalized Gaussian functionals of the first kind generalized Gaussian functionals of the second kind and the Fourier transform. Part 4 Stochastic analysis and quantum mechanics: systems with changeable numbers of particles the random statistics local intersection times. Part 5 Equations with random operators: estimation of the moments of multi-linear forms from white noise equations with random operators under moment conditions boundary value problems stochastic calculus and partial differential equations of the first order.