The Extended Stochastic Integral In Linear Spaces With Differentiable Measures And Related Topics

Download or read book The Extended Stochastic Integral In Linear Spaces With Differentiable Measures And Related Topics written by Nicolai Victorovich Norin and published by World Scientific. This book was released on 1996-08-30 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Wiener spaces; and then discusses in detail the ESI for the Wiener 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.