This volume discusses the extended stochastic integral (ESI) (or Skorokhod-Hitsuda integral) and its relation to the logarithmic derivative of differentiable measure along the vector or operator field. In addition, the theory of surface measures and the theory of heat potentials in infinite-dimensional spaces are discussed. These theories are closely related to ESI. It starts with an account of classic stochastic analysis in the Weiner spaces; and then discusses in detail the ESI for the Weiner measure including properties of this integral understood as a process. Moreover, the ESI with a nonrandom kernel is investigated. Some chapters are devoted to the definition and the investigation of properties of the ESI for Gaussian and differentiable measures. Surface measures in Banach spaces and heat potentials theory in Hilbert space are also discussed.
Stochastic calculus in Weiner space
extended stochastic integral in Weiner space
randomized extended stochastic integrals with jumps
introduction to the theory of differentiable measures
extended vector stochastic integral in Sobolev spaces of Weiner functionals
stochastic integrals and differentiable meaures
differential properties of mixtures of Gaussian measures
surface measures in Banach space
heat potentials on Hilbert space.